p-group, metabelian, nilpotent (class 3), monomial, rational
Aliases: C23.9C24, C24.130C23, 2+ 1+4.15C22, (C2×D4)⋊27D4, (C2×Q8)⋊21D4, (C22×C4)⋊8D4, C2≀C22⋊5C2, C4.47C22≀C2, C23⋊C4⋊9C22, C23.28(C2×D4), C22≀C2⋊2C22, C2.C25⋊4C2, (C2×D4).43C23, C22⋊C4.2C23, C22.29C24⋊7C2, (C22×D4)⋊22C22, C22.43(C22×D4), C42⋊C2⋊13C22, (C22×C4).285C23, C23.C23⋊19C2, (C2×C4).29(C2×D4), C2.64(C2×C22≀C2), (C2×C4○D4).112C22, SmallGroup(128,1759)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C23.9C24
G = < a,b,c,d,e,f,g | a2=b2=c2=d2=e2=f2=1, g2=c, ab=ba, faf=ac=ca, ede=ad=da, ae=ea, ag=ga, ebe=bc=cb, fdf=bd=db, bf=fb, bg=gb, gdg-1=cd=dc, ce=ec, cf=fc, cg=gc, ef=fe, eg=ge, fg=gf >
Subgroups: 860 in 386 conjugacy classes, 106 normal (8 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C2×C4, C2×C4, D4, Q8, C23, C23, C23, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, C24, C23⋊C4, C42⋊C2, C22≀C2, C4⋊D4, C4.4D4, C4⋊1D4, C22×D4, C2×C4○D4, C2×C4○D4, 2+ 1+4, 2+ 1+4, 2- 1+4, C23.C23, C2≀C22, C22.29C24, C2.C25, C23.9C24
Quotients: C1, C2, C22, D4, C23, C2×D4, C24, C22≀C2, C22×D4, C2×C22≀C2, C23.9C24
Character table of C23.9C24
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 2J | 2K | 2L | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | |
| size | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 8 | 8 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 2 |
| ρ3 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | linear of order 2 |
| ρ4 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | linear of order 2 |
| ρ5 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | linear of order 2 |
| ρ6 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | 1 | linear of order 2 |
| ρ7 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | linear of order 2 |
| ρ8 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | linear of order 2 |
| ρ9 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | -1 | 1 | 1 | 1 | -1 | linear of order 2 |
| ρ10 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | 1 | linear of order 2 |
| ρ11 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | linear of order 2 |
| ρ12 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | linear of order 2 |
| ρ13 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | linear of order 2 |
| ρ14 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | linear of order 2 |
| ρ15 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | linear of order 2 |
| ρ16 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | linear of order 2 |
| ρ17 | 2 | 2 | -2 | -2 | 2 | 0 | 0 | -2 | 0 | 2 | 0 | 0 | 0 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ18 | 2 | 2 | 2 | -2 | -2 | 0 | 2 | 0 | 0 | 0 | 2 | 0 | 0 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ19 | 2 | 2 | -2 | 2 | -2 | 2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | -2 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ20 | 2 | 2 | -2 | -2 | 2 | 0 | 0 | -2 | 0 | -2 | 0 | 0 | 0 | -2 | -2 | 2 | 2 | 2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ21 | 2 | 2 | 2 | -2 | -2 | 0 | -2 | 0 | 0 | 0 | -2 | 0 | 0 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ22 | 2 | 2 | -2 | 2 | -2 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 2 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ23 | 2 | 2 | 2 | -2 | -2 | 0 | 2 | 0 | 0 | 0 | -2 | 0 | 0 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ24 | 2 | 2 | -2 | -2 | 2 | 0 | 0 | 2 | 0 | 2 | 0 | 0 | 0 | -2 | -2 | 2 | 2 | -2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ25 | 2 | 2 | -2 | 2 | -2 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 2 | 0 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ26 | 2 | 2 | 2 | -2 | -2 | 0 | -2 | 0 | 0 | 0 | 2 | 0 | 0 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ27 | 2 | 2 | -2 | 2 | -2 | -2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | -2 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ28 | 2 | 2 | -2 | -2 | 2 | 0 | 0 | 2 | 0 | -2 | 0 | 0 | 0 | 2 | 2 | -2 | -2 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ29 | 8 | -8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal faithful |
►On 16 points - transitive group 16T239
Generators in S16
(1 11)(2 12)(3 9)(4 10)(5 14)(6 15)(7 16)(8 13)
(5 7)(6 8)(13 15)(14 16)
(1 3)(2 4)(5 7)(6 8)(9 11)(10 12)(13 15)(14 16)
(2 4)(5 14)(6 13)(7 16)(8 15)(10 12)
(1 14)(2 15)(3 16)(4 13)(5 11)(6 12)(7 9)(8 10)
(5 7)(6 8)(9 11)(10 12)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)
G:=sub<Sym(16)| (1,11)(2,12)(3,9)(4,10)(5,14)(6,15)(7,16)(8,13), (5,7)(6,8)(13,15)(14,16), (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16), (2,4)(5,14)(6,13)(7,16)(8,15)(10,12), (1,14)(2,15)(3,16)(4,13)(5,11)(6,12)(7,9)(8,10), (5,7)(6,8)(9,11)(10,12), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)>;
G:=Group( (1,11)(2,12)(3,9)(4,10)(5,14)(6,15)(7,16)(8,13), (5,7)(6,8)(13,15)(14,16), (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16), (2,4)(5,14)(6,13)(7,16)(8,15)(10,12), (1,14)(2,15)(3,16)(4,13)(5,11)(6,12)(7,9)(8,10), (5,7)(6,8)(9,11)(10,12), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16) );
G=PermutationGroup([[(1,11),(2,12),(3,9),(4,10),(5,14),(6,15),(7,16),(8,13)], [(5,7),(6,8),(13,15),(14,16)], [(1,3),(2,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16)], [(2,4),(5,14),(6,13),(7,16),(8,15),(10,12)], [(1,14),(2,15),(3,16),(4,13),(5,11),(6,12),(7,9),(8,10)], [(5,7),(6,8),(9,11),(10,12)], [(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16)]])
G:=TransitiveGroup(16,239);
►On 16 points - transitive group 16T313
Generators in S16
(5 7)(6 8)(13 15)(14 16)
(9 11)(10 12)(13 15)(14 16)
(1 3)(2 4)(5 7)(6 8)(9 11)(10 12)(13 15)(14 16)
(2 4)(6 8)(10 12)(13 15)
(1 11)(2 12)(3 9)(4 10)(5 13)(6 14)(7 15)(8 16)
(1 7)(2 8)(3 5)(4 6)(9 13)(10 14)(11 15)(12 16)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)
G:=sub<Sym(16)| (5,7)(6,8)(13,15)(14,16), (9,11)(10,12)(13,15)(14,16), (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16), (2,4)(6,8)(10,12)(13,15), (1,11)(2,12)(3,9)(4,10)(5,13)(6,14)(7,15)(8,16), (1,7)(2,8)(3,5)(4,6)(9,13)(10,14)(11,15)(12,16), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)>;
G:=Group( (5,7)(6,8)(13,15)(14,16), (9,11)(10,12)(13,15)(14,16), (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16), (2,4)(6,8)(10,12)(13,15), (1,11)(2,12)(3,9)(4,10)(5,13)(6,14)(7,15)(8,16), (1,7)(2,8)(3,5)(4,6)(9,13)(10,14)(11,15)(12,16), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16) );
G=PermutationGroup([[(5,7),(6,8),(13,15),(14,16)], [(9,11),(10,12),(13,15),(14,16)], [(1,3),(2,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16)], [(2,4),(6,8),(10,12),(13,15)], [(1,11),(2,12),(3,9),(4,10),(5,13),(6,14),(7,15),(8,16)], [(1,7),(2,8),(3,5),(4,6),(9,13),(10,14),(11,15),(12,16)], [(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16)]])
G:=TransitiveGroup(16,313);
Matrix representation of C23.9C24 ►in GL8(ℤ)
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | -1 | 0 | 0 |
| 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| 0 | 0 | 0 | 0 | 0 | 0 | -1 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | -1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | -1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | -1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | -1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | -1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| 0 | 0 | 0 | 0 | 0 | 0 | -1 | 0 |
| 0 | 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 | 1 | 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 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | -1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | -1 | 0 | 0 |
G:=sub<GL(8,Integers())| [0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0],[0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0],[-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0],[0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0],[0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0] >;
C23.9C24 in GAP, Magma, Sage, TeX
C_2^3._9C_2^4
% in TeX
G:=Group("C2^3.9C2^4"); // GroupNames label
G:=SmallGroup(128,1759);
// by ID
G=gap.SmallGroup(128,1759);
# by ID
G:=PCGroup([7,-2,2,2,2,-2,2,-2,253,758,2019,248,718,2028]);
// Polycyclic
G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=d^2=e^2=f^2=1,g^2=c,a*b=b*a,f*a*f=a*c=c*a,e*d*e=a*d=d*a,a*e=e*a,a*g=g*a,e*b*e=b*c=c*b,f*d*f=b*d=d*b,b*f=f*b,b*g=g*b,g*d*g^-1=c*d=d*c,c*e=e*c,c*f=f*c,c*g=g*c,e*f=f*e,e*g=g*e,f*g=g*f>;
// generators/relations
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