metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C7⋊C8⋊22D4, (C2×C14)⋊3D8, C4⋊D4⋊3D7, C7⋊3(C8⋊7D4), C4⋊C4.58D14, C14.55(C2×D8), C4.170(D4×D7), C28⋊7D4⋊23C2, C22⋊1(D4⋊D7), (C2×D4).38D14, (C2×C28).263D4, C28.147(C2×D4), C14.D8⋊35C2, C14.97(C4○D8), D4⋊Dic7⋊15C2, C28.Q8⋊36C2, (C22×C14).84D4, C28.183(C4○D4), C4.59(D4⋊2D7), C14.93(C4⋊D4), (C2×C28).357C23, (D4×C14).54C22, (C2×D28).97C22, (C22×C4).340D14, C23.39(C7⋊D4), C4⋊Dic7.142C22, C2.14(Dic7⋊D4), C2.16(D4.8D14), (C22×C28).161C22, (C22×C7⋊C8)⋊3C2, (C2×D4⋊D7)⋊10C2, (C7×C4⋊D4)⋊3C2, C2.10(C2×D4⋊D7), (C2×C14).488(C2×D4), (C2×C7⋊C8).248C22, (C2×C4).105(C7⋊D4), (C7×C4⋊C4).105C22, (C2×C4).457(C22×D7), C22.163(C2×C7⋊D4), SmallGroup(448,572)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7⋊C8⋊22D4
G = < a,b,c,d | a7=b8=c4=d2=1, bab-1=a-1, ac=ca, ad=da, cbc-1=b-1, bd=db, dcd=c-1 >
Subgroups: 684 in 134 conjugacy classes, 45 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, D8, C22×C4, C2×D4, C2×D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, D4⋊C4, C2.D8, C4⋊D4, C4⋊D4, C22×C8, C2×D8, C7⋊C8, C7⋊C8, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22×C14, C8⋊7D4, C2×C7⋊C8, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, D4⋊D7, C7×C22⋊C4, C7×C4⋊C4, C2×D28, C2×C7⋊D4, C22×C28, D4×C14, D4×C14, C28.Q8, C14.D8, D4⋊Dic7, C22×C7⋊C8, C28⋊7D4, C2×D4⋊D7, C7×C4⋊D4, C7⋊C8⋊22D4
Quotients: C1, C2, C22, D4, C23, D7, D8, C2×D4, C4○D4, D14, C4⋊D4, C2×D8, C4○D8, C7⋊D4, C22×D7, C8⋊7D4, D4⋊D7, D4×D7, D4⋊2D7, C2×C7⋊D4, C2×D4⋊D7, Dic7⋊D4, D4.8D14, C7⋊C8⋊22D4
►On 224 points
Generators in S224
(1 184 33 88 126 28 214)(2 215 29 127 81 34 177)(3 178 35 82 128 30 216)(4 209 31 121 83 36 179)(5 180 37 84 122 32 210)(6 211 25 123 85 38 181)(7 182 39 86 124 26 212)(8 213 27 125 87 40 183)(9 195 156 20 170 93 68)(10 69 94 171 21 157 196)(11 197 158 22 172 95 70)(12 71 96 173 23 159 198)(13 199 160 24 174 89 72)(14 65 90 175 17 153 200)(15 193 154 18 176 91 66)(16 67 92 169 19 155 194)(41 77 115 219 187 110 148)(42 149 111 188 220 116 78)(43 79 117 221 189 112 150)(44 151 105 190 222 118 80)(45 73 119 223 191 106 152)(46 145 107 192 224 120 74)(47 75 113 217 185 108 146)(48 147 109 186 218 114 76)(49 207 142 104 165 63 129)(50 130 64 166 97 143 208)(51 201 144 98 167 57 131)(52 132 58 168 99 137 202)(53 203 138 100 161 59 133)(54 134 60 162 101 139 204)(55 205 140 102 163 61 135)(56 136 62 164 103 141 206)
(1 2 3 4 5 6 7 8)(9 10 11 12 13 14 15 16)(17 18 19 20 21 22 23 24)(25 26 27 28 29 30 31 32)(33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48)(49 50 51 52 53 54 55 56)(57 58 59 60 61 62 63 64)(65 66 67 68 69 70 71 72)(73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88)(89 90 91 92 93 94 95 96)(97 98 99 100 101 102 103 104)(105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128)(129 130 131 132 133 134 135 136)(137 138 139 140 141 142 143 144)(145 146 147 148 149 150 151 152)(153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176)(177 178 179 180 181 182 183 184)(185 186 187 188 189 190 191 192)(193 194 195 196 197 198 199 200)(201 202 203 204 205 206 207 208)(209 210 211 212 213 214 215 216)(217 218 219 220 221 222 223 224)
(1 156 47 165)(2 155 48 164)(3 154 41 163)(4 153 42 162)(5 160 43 161)(6 159 44 168)(7 158 45 167)(8 157 46 166)(9 108 142 28)(10 107 143 27)(11 106 144 26)(12 105 137 25)(13 112 138 32)(14 111 139 31)(15 110 140 30)(16 109 141 29)(17 78 60 179)(18 77 61 178)(19 76 62 177)(20 75 63 184)(21 74 64 183)(22 73 57 182)(23 80 58 181)(24 79 59 180)(33 170 113 129)(34 169 114 136)(35 176 115 135)(36 175 116 134)(37 174 117 133)(38 173 118 132)(39 172 119 131)(40 171 120 130)(49 88 93 217)(50 87 94 224)(51 86 95 223)(52 85 96 222)(53 84 89 221)(54 83 90 220)(55 82 91 219)(56 81 92 218)(65 188 204 121)(66 187 205 128)(67 186 206 127)(68 185 207 126)(69 192 208 125)(70 191 201 124)(71 190 202 123)(72 189 203 122)(97 213 196 145)(98 212 197 152)(99 211 198 151)(100 210 199 150)(101 209 200 149)(102 216 193 148)(103 215 194 147)(104 214 195 146)
(9 142)(10 143)(11 144)(12 137)(13 138)(14 139)(15 140)(16 141)(17 60)(18 61)(19 62)(20 63)(21 64)(22 57)(23 58)(24 59)(49 93)(50 94)(51 95)(52 96)(53 89)(54 90)(55 91)(56 92)(65 204)(66 205)(67 206)(68 207)(69 208)(70 201)(71 202)(72 203)(97 196)(98 197)(99 198)(100 199)(101 200)(102 193)(103 194)(104 195)(129 170)(130 171)(131 172)(132 173)(133 174)(134 175)(135 176)(136 169)(153 162)(154 163)(155 164)(156 165)(157 166)(158 167)(159 168)(160 161)
G:=sub<Sym(224)| (1,184,33,88,126,28,214)(2,215,29,127,81,34,177)(3,178,35,82,128,30,216)(4,209,31,121,83,36,179)(5,180,37,84,122,32,210)(6,211,25,123,85,38,181)(7,182,39,86,124,26,212)(8,213,27,125,87,40,183)(9,195,156,20,170,93,68)(10,69,94,171,21,157,196)(11,197,158,22,172,95,70)(12,71,96,173,23,159,198)(13,199,160,24,174,89,72)(14,65,90,175,17,153,200)(15,193,154,18,176,91,66)(16,67,92,169,19,155,194)(41,77,115,219,187,110,148)(42,149,111,188,220,116,78)(43,79,117,221,189,112,150)(44,151,105,190,222,118,80)(45,73,119,223,191,106,152)(46,145,107,192,224,120,74)(47,75,113,217,185,108,146)(48,147,109,186,218,114,76)(49,207,142,104,165,63,129)(50,130,64,166,97,143,208)(51,201,144,98,167,57,131)(52,132,58,168,99,137,202)(53,203,138,100,161,59,133)(54,134,60,162,101,139,204)(55,205,140,102,163,61,135)(56,136,62,164,103,141,206), (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136)(137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152)(153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184)(185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224), (1,156,47,165)(2,155,48,164)(3,154,41,163)(4,153,42,162)(5,160,43,161)(6,159,44,168)(7,158,45,167)(8,157,46,166)(9,108,142,28)(10,107,143,27)(11,106,144,26)(12,105,137,25)(13,112,138,32)(14,111,139,31)(15,110,140,30)(16,109,141,29)(17,78,60,179)(18,77,61,178)(19,76,62,177)(20,75,63,184)(21,74,64,183)(22,73,57,182)(23,80,58,181)(24,79,59,180)(33,170,113,129)(34,169,114,136)(35,176,115,135)(36,175,116,134)(37,174,117,133)(38,173,118,132)(39,172,119,131)(40,171,120,130)(49,88,93,217)(50,87,94,224)(51,86,95,223)(52,85,96,222)(53,84,89,221)(54,83,90,220)(55,82,91,219)(56,81,92,218)(65,188,204,121)(66,187,205,128)(67,186,206,127)(68,185,207,126)(69,192,208,125)(70,191,201,124)(71,190,202,123)(72,189,203,122)(97,213,196,145)(98,212,197,152)(99,211,198,151)(100,210,199,150)(101,209,200,149)(102,216,193,148)(103,215,194,147)(104,214,195,146), (9,142)(10,143)(11,144)(12,137)(13,138)(14,139)(15,140)(16,141)(17,60)(18,61)(19,62)(20,63)(21,64)(22,57)(23,58)(24,59)(49,93)(50,94)(51,95)(52,96)(53,89)(54,90)(55,91)(56,92)(65,204)(66,205)(67,206)(68,207)(69,208)(70,201)(71,202)(72,203)(97,196)(98,197)(99,198)(100,199)(101,200)(102,193)(103,194)(104,195)(129,170)(130,171)(131,172)(132,173)(133,174)(134,175)(135,176)(136,169)(153,162)(154,163)(155,164)(156,165)(157,166)(158,167)(159,168)(160,161)>;
G:=Group( (1,184,33,88,126,28,214)(2,215,29,127,81,34,177)(3,178,35,82,128,30,216)(4,209,31,121,83,36,179)(5,180,37,84,122,32,210)(6,211,25,123,85,38,181)(7,182,39,86,124,26,212)(8,213,27,125,87,40,183)(9,195,156,20,170,93,68)(10,69,94,171,21,157,196)(11,197,158,22,172,95,70)(12,71,96,173,23,159,198)(13,199,160,24,174,89,72)(14,65,90,175,17,153,200)(15,193,154,18,176,91,66)(16,67,92,169,19,155,194)(41,77,115,219,187,110,148)(42,149,111,188,220,116,78)(43,79,117,221,189,112,150)(44,151,105,190,222,118,80)(45,73,119,223,191,106,152)(46,145,107,192,224,120,74)(47,75,113,217,185,108,146)(48,147,109,186,218,114,76)(49,207,142,104,165,63,129)(50,130,64,166,97,143,208)(51,201,144,98,167,57,131)(52,132,58,168,99,137,202)(53,203,138,100,161,59,133)(54,134,60,162,101,139,204)(55,205,140,102,163,61,135)(56,136,62,164,103,141,206), (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136)(137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152)(153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184)(185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224), (1,156,47,165)(2,155,48,164)(3,154,41,163)(4,153,42,162)(5,160,43,161)(6,159,44,168)(7,158,45,167)(8,157,46,166)(9,108,142,28)(10,107,143,27)(11,106,144,26)(12,105,137,25)(13,112,138,32)(14,111,139,31)(15,110,140,30)(16,109,141,29)(17,78,60,179)(18,77,61,178)(19,76,62,177)(20,75,63,184)(21,74,64,183)(22,73,57,182)(23,80,58,181)(24,79,59,180)(33,170,113,129)(34,169,114,136)(35,176,115,135)(36,175,116,134)(37,174,117,133)(38,173,118,132)(39,172,119,131)(40,171,120,130)(49,88,93,217)(50,87,94,224)(51,86,95,223)(52,85,96,222)(53,84,89,221)(54,83,90,220)(55,82,91,219)(56,81,92,218)(65,188,204,121)(66,187,205,128)(67,186,206,127)(68,185,207,126)(69,192,208,125)(70,191,201,124)(71,190,202,123)(72,189,203,122)(97,213,196,145)(98,212,197,152)(99,211,198,151)(100,210,199,150)(101,209,200,149)(102,216,193,148)(103,215,194,147)(104,214,195,146), (9,142)(10,143)(11,144)(12,137)(13,138)(14,139)(15,140)(16,141)(17,60)(18,61)(19,62)(20,63)(21,64)(22,57)(23,58)(24,59)(49,93)(50,94)(51,95)(52,96)(53,89)(54,90)(55,91)(56,92)(65,204)(66,205)(67,206)(68,207)(69,208)(70,201)(71,202)(72,203)(97,196)(98,197)(99,198)(100,199)(101,200)(102,193)(103,194)(104,195)(129,170)(130,171)(131,172)(132,173)(133,174)(134,175)(135,176)(136,169)(153,162)(154,163)(155,164)(156,165)(157,166)(158,167)(159,168)(160,161) );
G=PermutationGroup([[(1,184,33,88,126,28,214),(2,215,29,127,81,34,177),(3,178,35,82,128,30,216),(4,209,31,121,83,36,179),(5,180,37,84,122,32,210),(6,211,25,123,85,38,181),(7,182,39,86,124,26,212),(8,213,27,125,87,40,183),(9,195,156,20,170,93,68),(10,69,94,171,21,157,196),(11,197,158,22,172,95,70),(12,71,96,173,23,159,198),(13,199,160,24,174,89,72),(14,65,90,175,17,153,200),(15,193,154,18,176,91,66),(16,67,92,169,19,155,194),(41,77,115,219,187,110,148),(42,149,111,188,220,116,78),(43,79,117,221,189,112,150),(44,151,105,190,222,118,80),(45,73,119,223,191,106,152),(46,145,107,192,224,120,74),(47,75,113,217,185,108,146),(48,147,109,186,218,114,76),(49,207,142,104,165,63,129),(50,130,64,166,97,143,208),(51,201,144,98,167,57,131),(52,132,58,168,99,137,202),(53,203,138,100,161,59,133),(54,134,60,162,101,139,204),(55,205,140,102,163,61,135),(56,136,62,164,103,141,206)], [(1,2,3,4,5,6,7,8),(9,10,11,12,13,14,15,16),(17,18,19,20,21,22,23,24),(25,26,27,28,29,30,31,32),(33,34,35,36,37,38,39,40),(41,42,43,44,45,46,47,48),(49,50,51,52,53,54,55,56),(57,58,59,60,61,62,63,64),(65,66,67,68,69,70,71,72),(73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88),(89,90,91,92,93,94,95,96),(97,98,99,100,101,102,103,104),(105,106,107,108,109,110,111,112),(113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128),(129,130,131,132,133,134,135,136),(137,138,139,140,141,142,143,144),(145,146,147,148,149,150,151,152),(153,154,155,156,157,158,159,160),(161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176),(177,178,179,180,181,182,183,184),(185,186,187,188,189,190,191,192),(193,194,195,196,197,198,199,200),(201,202,203,204,205,206,207,208),(209,210,211,212,213,214,215,216),(217,218,219,220,221,222,223,224)], [(1,156,47,165),(2,155,48,164),(3,154,41,163),(4,153,42,162),(5,160,43,161),(6,159,44,168),(7,158,45,167),(8,157,46,166),(9,108,142,28),(10,107,143,27),(11,106,144,26),(12,105,137,25),(13,112,138,32),(14,111,139,31),(15,110,140,30),(16,109,141,29),(17,78,60,179),(18,77,61,178),(19,76,62,177),(20,75,63,184),(21,74,64,183),(22,73,57,182),(23,80,58,181),(24,79,59,180),(33,170,113,129),(34,169,114,136),(35,176,115,135),(36,175,116,134),(37,174,117,133),(38,173,118,132),(39,172,119,131),(40,171,120,130),(49,88,93,217),(50,87,94,224),(51,86,95,223),(52,85,96,222),(53,84,89,221),(54,83,90,220),(55,82,91,219),(56,81,92,218),(65,188,204,121),(66,187,205,128),(67,186,206,127),(68,185,207,126),(69,192,208,125),(70,191,201,124),(71,190,202,123),(72,189,203,122),(97,213,196,145),(98,212,197,152),(99,211,198,151),(100,210,199,150),(101,209,200,149),(102,216,193,148),(103,215,194,147),(104,214,195,146)], [(9,142),(10,143),(11,144),(12,137),(13,138),(14,139),(15,140),(16,141),(17,60),(18,61),(19,62),(20,63),(21,64),(22,57),(23,58),(24,59),(49,93),(50,94),(51,95),(52,96),(53,89),(54,90),(55,91),(56,92),(65,204),(66,205),(67,206),(68,207),(69,208),(70,201),(71,202),(72,203),(97,196),(98,197),(99,198),(100,199),(101,200),(102,193),(103,194),(104,195),(129,170),(130,171),(131,172),(132,173),(133,174),(134,175),(135,176),(136,169),(153,162),(154,163),(155,164),(156,165),(157,166),(158,167),(159,168),(160,161)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14I | 14J | ··· | 14O | 14P | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 8 | 56 | 2 | 2 | 2 | 2 | 8 | 56 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D7 | C4○D4 | D8 | D14 | D14 | D14 | C4○D8 | C7⋊D4 | C7⋊D4 | D4×D7 | D4⋊2D7 | D4⋊D7 | D4.8D14 |
| kernel | C7⋊C8⋊22D4 | C28.Q8 | C14.D8 | D4⋊Dic7 | C22×C7⋊C8 | C28⋊7D4 | C2×D4⋊D7 | C7×C4⋊D4 | C7⋊C8 | C2×C28 | C22×C14 | C4⋊D4 | C28 | C2×C14 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C2×C4 | C23 | C4 | C4 | C22 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 3 | 2 | 4 | 3 | 3 | 3 | 4 | 6 | 6 | 3 | 3 | 6 | 6 |
Matrix representation of C7⋊C8⋊22D4 ►in GL6(𝔽113)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 87 | 0 | 0 |
| 0 | 0 | 1 | 25 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 44 | 0 | 0 | 0 | 0 | 0 |
| 0 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 109 | 112 | 0 | 0 |
| 0 | 0 | 17 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 44 | 0 | 0 |
| 0 | 0 | 7 | 91 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,1,0,0,0,0,87,25,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[44,0,0,0,0,0,0,18,0,0,0,0,0,0,109,17,0,0,0,0,112,4,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[0,1,0,0,0,0,112,0,0,0,0,0,0,0,22,7,0,0,0,0,44,91,0,0,0,0,0,0,0,1,0,0,0,0,112,0],[1,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,112] >;
C7⋊C8⋊22D4 in GAP, Magma, Sage, TeX
C_7\rtimes C_8\rtimes_{22}D_4 % in TeX
G:=Group("C7:C8:22D4"); // GroupNames label
G:=SmallGroup(448,572);
// by ID
G=gap.SmallGroup(448,572);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,254,219,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^7=b^8=c^4=d^2=1,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d=c^-1>;
// generators/relations