C2^3:2D4:C3 - GroupNames

G = C₂³⋊₂D₄⋊C₃ order 192 = 2⁶·3

The semidirect product of C₂³⋊₂D₄ and C₃ acting faithfully

Aliases: C₂³⋊₂D₄⋊C₃, (C₂²×C₄).₃A₄, C₂³.₁₄(C₂×A₄), C₂³.₃A₄⋊₁C₂, C₂².₂(C₄.A₄), C₂.₂(C₂³.A₄), C₂.C₄².₂C₆, SmallGroup(192,194)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₂ — C₂.C₄² — C₂³⋊₂D₄⋊C₃

Chief series

C₁ — C₂ — C₂³ — C₂.C₄² — C₂³.₃A₄ — C₂³⋊₂D₄⋊C₃

Lower central

C₂.C₄² — C₂³⋊₂D₄⋊C₃

Upper central

C₁ — C₂

Generators and relations for C₂³⋊₂D₄⋊C₃
G = < a,b,c,d,e,f | a²=b²=c²=d⁴=e²=f³=1, eae=ab=ba, ac=ca, dad^-1=abc, faf^-1=ec=ce, bc=cb, bd=db, be=eb, fbf^-1=d², cd=dc, fcf^-1=b, ede=d^-1, fdf^-1=abcd^-1e, fef^-1=cde >

Subgroups: 379 in 67 conjugacy classes, 9 normal (all characteristic)
C₁, C₂, C₂, C₃, C₄, C₂², C₂², C₆, C₂×C₄, D₄, C₂³, C₂³, C₁₂, A₄, C₂²⋊C₄, C₂²×C₄, C₂²×C₄, C₂×D₄, C₂⁴, C₂×A₄, C₂.C₄², C₂×C₂²⋊C₄, C₂²×D₄, C₄×A₄, C₂³⋊₂D₄, C₂³.₃A₄, C₂³⋊₂D₄⋊C₃
Quotients: C₁, C₂, C₃, C₆, A₄, C₂×A₄, C₄.A₄, C₂³.A₄, C₂³⋊₂D₄⋊C₃

Character table of C₂³⋊₂D₄⋊C₃

class	1	2A	2B	2C	2D	2E	3A	3B	4A	4B	4C	4D	6A	6B	12A	12B	12C	12D
size	1	1	3	3	12	12	16	16	4	4	12	12	16	16	16	16	16	16
ρ₁	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	linear of order 2
ρ₃	1	1	1	1	1	1	ζ₃²	ζ₃	1	1	1	1	ζ₃	ζ₃²	ζ₃²	ζ₃²	ζ₃	ζ₃	linear of order 3
ρ₄	1	1	1	1	-1	-1	ζ₃²	ζ₃	-1	-1	1	1	ζ₃	ζ₃²	ζ₆	ζ₆	ζ₆⁵	ζ₆⁵	linear of order 6
ρ₅	1	1	1	1	-1	-1	ζ₃	ζ₃²	-1	-1	1	1	ζ₃²	ζ₃	ζ₆⁵	ζ₆⁵	ζ₆	ζ₆	linear of order 6
ρ₆	1	1	1	1	1	1	ζ₃	ζ₃²	1	1	1	1	ζ₃²	ζ₃	ζ₃	ζ₃	ζ₃²	ζ₃²	linear of order 3
ρ₇	2	-2	2	-2	0	0	-1	-1	-2i	2i	0	0	1	1	i	-i	i	-i	complex lifted from C₄.A₄
ρ₈	2	-2	2	-2	0	0	-1	-1	2i	-2i	0	0	1	1	-i	i	-i	i	complex lifted from C₄.A₄
ρ₉	2	-2	2	-2	0	0	ζ₆	ζ₆⁵	-2i	2i	0	0	ζ₃	ζ₃²	ζ₄ζ₃²	ζ₄³ζ₃²	ζ₄ζ₃	ζ₄³ζ₃	complex lifted from C₄.A₄
ρ₁₀	2	-2	2	-2	0	0	ζ₆	ζ₆⁵	2i	-2i	0	0	ζ₃	ζ₃²	ζ₄³ζ₃²	ζ₄ζ₃²	ζ₄³ζ₃	ζ₄ζ₃	complex lifted from C₄.A₄
ρ₁₁	2	-2	2	-2	0	0	ζ₆⁵	ζ₆	2i	-2i	0	0	ζ₃²	ζ₃	ζ₄³ζ₃	ζ₄ζ₃	ζ₄³ζ₃²	ζ₄ζ₃²	complex lifted from C₄.A₄
ρ₁₂	2	-2	2	-2	0	0	ζ₆⁵	ζ₆	-2i	2i	0	0	ζ₃²	ζ₃	ζ₄ζ₃	ζ₄³ζ₃	ζ₄ζ₃²	ζ₄³ζ₃²	complex lifted from C₄.A₄
ρ₁₃	3	3	3	3	1	1	0	0	-3	-3	-1	-1	0	0	0	0	0	0	orthogonal lifted from C₂×A₄
ρ₁₄	3	3	3	3	-1	-1	0	0	3	3	-1	-1	0	0	0	0	0	0	orthogonal lifted from A₄
ρ₁₅	6	-6	-2	2	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal faithful
ρ₁₆	6	6	-2	-2	0	0	0	0	0	0	-2	2	0	0	0	0	0	0	orthogonal lifted from C₂³.A₄
ρ₁₇	6	-6	-2	2	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal faithful
ρ₁₈	6	6	-2	-2	0	0	0	0	0	0	2	-2	0	0	0	0	0	0	orthogonal lifted from C₂³.A₄

Permutation representations of C₂³⋊₂D₄⋊C₃
►On 12 points - transitive group 12T104

Generators in S₁₂

(1 3)(2 4)(6 8)(9 11)(10 12)

(1 2)(3 4)

(5 7)(6 8)

(3 4)(5 6)(7 8)(9 10 11 12)

(3 4)(9 10)(11 12)

(1 7 11)(2 5 9)(3 6 12)(4 8 10)

G:=sub<Sym(12)| (1,3)(2,4)(6,8)(9,11)(10,12), (1,2)(3,4), (5,7)(6,8), (3,4)(5,6)(7,8)(9,10,11,12), (3,4)(9,10)(11,12), (1,7,11)(2,5,9)(3,6,12)(4,8,10)>;

G:=Group( (1,3)(2,4)(6,8)(9,11)(10,12), (1,2)(3,4), (5,7)(6,8), (3,4)(5,6)(7,8)(9,10,11,12), (3,4)(9,10)(11,12), (1,7,11)(2,5,9)(3,6,12)(4,8,10) );

G=PermutationGroup([[(1,3),(2,4),(6,8),(9,11),(10,12)], [(1,2),(3,4)], [(5,7),(6,8)], [(3,4),(5,6),(7,8),(9,10,11,12)], [(3,4),(9,10),(11,12)], [(1,7,11),(2,5,9),(3,6,12),(4,8,10)]])

G:=TransitiveGroup(12,104);

►On 24 points - transitive group 24T496

Generators in S₂₄

(1 10)(2 8)(3 9)(4 7)(5 13)(6 16)(11 15)(12 14)(17 23)(18 24)(19 21)(20 22)

(1 3)(2 4)(7 8)(9 10)

(5 11)(6 12)(13 15)(14 16)

(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)(17 18 19 20)(21 22 23 24)

(1 2)(3 4)(5 15)(6 16)(7 10)(8 9)(11 13)(12 14)(17 24)(18 23)(19 22)(20 21)

(1 16 18)(2 6 22)(3 14 20)(4 12 24)(5 21 9)(7 15 17)(8 13 19)(10 11 23)

G:=sub<Sym(24)| (1,10)(2,8)(3,9)(4,7)(5,13)(6,16)(11,15)(12,14)(17,23)(18,24)(19,21)(20,22), (1,3)(2,4)(7,8)(9,10), (5,11)(6,12)(13,15)(14,16), (5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(21,22,23,24), (1,2)(3,4)(5,15)(6,16)(7,10)(8,9)(11,13)(12,14)(17,24)(18,23)(19,22)(20,21), (1,16,18)(2,6,22)(3,14,20)(4,12,24)(5,21,9)(7,15,17)(8,13,19)(10,11,23)>;

G:=Group( (1,10)(2,8)(3,9)(4,7)(5,13)(6,16)(11,15)(12,14)(17,23)(18,24)(19,21)(20,22), (1,3)(2,4)(7,8)(9,10), (5,11)(6,12)(13,15)(14,16), (5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(21,22,23,24), (1,2)(3,4)(5,15)(6,16)(7,10)(8,9)(11,13)(12,14)(17,24)(18,23)(19,22)(20,21), (1,16,18)(2,6,22)(3,14,20)(4,12,24)(5,21,9)(7,15,17)(8,13,19)(10,11,23) );

G=PermutationGroup([[(1,10),(2,8),(3,9),(4,7),(5,13),(6,16),(11,15),(12,14),(17,23),(18,24),(19,21),(20,22)], [(1,3),(2,4),(7,8),(9,10)], [(5,11),(6,12),(13,15),(14,16)], [(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18,19,20),(21,22,23,24)], [(1,2),(3,4),(5,15),(6,16),(7,10),(8,9),(11,13),(12,14),(17,24),(18,23),(19,22),(20,21)], [(1,16,18),(2,6,22),(3,14,20),(4,12,24),(5,21,9),(7,15,17),(8,13,19),(10,11,23)]])

G:=TransitiveGroup(24,496);

►On 24 points - transitive group 24T497

Generators in S₂₄

(1 4)(2 5)(3 10)(6 9)(7 16)(8 14)(11 15)(12 13)(17 19)(18 20)(21 23)(22 24)

(1 9)(2 10)(3 5)(4 6)

(7 12)(8 11)(13 16)(14 15)

(1 2)(3 4)(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)(17 18 19 20)(21 22 23 24)

(1 2)(3 4)(5 6)(9 10)(17 24)(18 23)(19 22)(20 21)

(1 15 18)(2 11 22)(3 12 17)(4 13 23)(5 7 19)(6 16 21)(8 24 10)(9 14 20)

G:=sub<Sym(24)| (1,4)(2,5)(3,10)(6,9)(7,16)(8,14)(11,15)(12,13)(17,19)(18,20)(21,23)(22,24), (1,9)(2,10)(3,5)(4,6), (7,12)(8,11)(13,16)(14,15), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(21,22,23,24), (1,2)(3,4)(5,6)(9,10)(17,24)(18,23)(19,22)(20,21), (1,15,18)(2,11,22)(3,12,17)(4,13,23)(5,7,19)(6,16,21)(8,24,10)(9,14,20)>;

G:=Group( (1,4)(2,5)(3,10)(6,9)(7,16)(8,14)(11,15)(12,13)(17,19)(18,20)(21,23)(22,24), (1,9)(2,10)(3,5)(4,6), (7,12)(8,11)(13,16)(14,15), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(21,22,23,24), (1,2)(3,4)(5,6)(9,10)(17,24)(18,23)(19,22)(20,21), (1,15,18)(2,11,22)(3,12,17)(4,13,23)(5,7,19)(6,16,21)(8,24,10)(9,14,20) );

G=PermutationGroup([[(1,4),(2,5),(3,10),(6,9),(7,16),(8,14),(11,15),(12,13),(17,19),(18,20),(21,23),(22,24)], [(1,9),(2,10),(3,5),(4,6)], [(7,12),(8,11),(13,16),(14,15)], [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18,19,20),(21,22,23,24)], [(1,2),(3,4),(5,6),(9,10),(17,24),(18,23),(19,22),(20,21)], [(1,15,18),(2,11,22),(3,12,17),(4,13,23),(5,7,19),(6,16,21),(8,24,10),(9,14,20)]])

G:=TransitiveGroup(24,497);

►On 24 points - transitive group 24T498

Generators in S₂₄

(1 12)(3 15)(4 10)(5 16)(6 9)(7 14)(17 24)(18 21)(19 22)(20 23)

(1 12)(2 11)(7 14)(8 13)

(3 6)(4 5)(9 15)(10 16)

(1 2)(3 4)(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)(17 18 19 20)(21 22 23 24)

(1 8)(2 7)(3 4)(5 6)(9 16)(10 15)(11 14)(12 13)(18 20)(21 23)

(1 4 20)(2 15 22)(3 21 7)(5 18 12)(6 23 14)(8 10 17)(9 24 11)(13 16 19)

G:=sub<Sym(24)| (1,12)(3,15)(4,10)(5,16)(6,9)(7,14)(17,24)(18,21)(19,22)(20,23), (1,12)(2,11)(7,14)(8,13), (3,6)(4,5)(9,15)(10,16), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(21,22,23,24), (1,8)(2,7)(3,4)(5,6)(9,16)(10,15)(11,14)(12,13)(18,20)(21,23), (1,4,20)(2,15,22)(3,21,7)(5,18,12)(6,23,14)(8,10,17)(9,24,11)(13,16,19)>;

G:=Group( (1,12)(3,15)(4,10)(5,16)(6,9)(7,14)(17,24)(18,21)(19,22)(20,23), (1,12)(2,11)(7,14)(8,13), (3,6)(4,5)(9,15)(10,16), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(21,22,23,24), (1,8)(2,7)(3,4)(5,6)(9,16)(10,15)(11,14)(12,13)(18,20)(21,23), (1,4,20)(2,15,22)(3,21,7)(5,18,12)(6,23,14)(8,10,17)(9,24,11)(13,16,19) );

G=PermutationGroup([[(1,12),(3,15),(4,10),(5,16),(6,9),(7,14),(17,24),(18,21),(19,22),(20,23)], [(1,12),(2,11),(7,14),(8,13)], [(3,6),(4,5),(9,15),(10,16)], [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18,19,20),(21,22,23,24)], [(1,8),(2,7),(3,4),(5,6),(9,16),(10,15),(11,14),(12,13),(18,20),(21,23)], [(1,4,20),(2,15,22),(3,21,7),(5,18,12),(6,23,14),(8,10,17),(9,24,11),(13,16,19)]])

G:=TransitiveGroup(24,498);

►On 24 points - transitive group 24T499

Generators in S₂₄

(1 5)(2 6)(3 7)(4 8)(10 17)(12 19)(13 24)(15 22)

(1 4)(2 3)(5 8)(6 7)(9 20)(10 17)(11 18)(12 19)

(1 3)(2 4)(5 7)(6 8)(13 24)(14 21)(15 22)(16 23)

(5 6)(7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)

(1 2)(3 4)(5 7)(6 8)(9 19)(10 18)(11 17)(12 20)(13 24)(14 23)(15 22)(16 21)

(1 22 9)(2 13 18)(3 24 20)(4 15 11)(5 21 19)(6 16 10)(7 23 12)(8 14 17)

G:=sub<Sym(24)| (1,5)(2,6)(3,7)(4,8)(10,17)(12,19)(13,24)(15,22), (1,4)(2,3)(5,8)(6,7)(9,20)(10,17)(11,18)(12,19), (1,3)(2,4)(5,7)(6,8)(13,24)(14,21)(15,22)(16,23), (5,6)(7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24), (1,2)(3,4)(5,7)(6,8)(9,19)(10,18)(11,17)(12,20)(13,24)(14,23)(15,22)(16,21), (1,22,9)(2,13,18)(3,24,20)(4,15,11)(5,21,19)(6,16,10)(7,23,12)(8,14,17)>;

G:=Group( (1,5)(2,6)(3,7)(4,8)(10,17)(12,19)(13,24)(15,22), (1,4)(2,3)(5,8)(6,7)(9,20)(10,17)(11,18)(12,19), (1,3)(2,4)(5,7)(6,8)(13,24)(14,21)(15,22)(16,23), (5,6)(7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24), (1,2)(3,4)(5,7)(6,8)(9,19)(10,18)(11,17)(12,20)(13,24)(14,23)(15,22)(16,21), (1,22,9)(2,13,18)(3,24,20)(4,15,11)(5,21,19)(6,16,10)(7,23,12)(8,14,17) );

G=PermutationGroup([[(1,5),(2,6),(3,7),(4,8),(10,17),(12,19),(13,24),(15,22)], [(1,4),(2,3),(5,8),(6,7),(9,20),(10,17),(11,18),(12,19)], [(1,3),(2,4),(5,7),(6,8),(13,24),(14,21),(15,22),(16,23)], [(5,6),(7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24)], [(1,2),(3,4),(5,7),(6,8),(9,19),(10,18),(11,17),(12,20),(13,24),(14,23),(15,22),(16,21)], [(1,22,9),(2,13,18),(3,24,20),(4,15,11),(5,21,19),(6,16,10),(7,23,12),(8,14,17)]])

G:=TransitiveGroup(24,499);

►On 24 points - transitive group 24T500

Generators in S₂₄

(1 5)(2 4)(3 7)(6 8)(10 16)(12 14)(17 22)(18 20)(19 24)(21 23)

(1 8)(2 7)(3 4)(5 6)(17 24)(18 21)(19 22)(20 23)

(1 2)(3 6)(4 5)(7 8)(9 15)(10 16)(11 13)(12 14)

(1 2)(3 4)(5 6)(7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)

(1 2)(3 5)(4 6)(7 8)(9 11)(13 15)(17 21)(18 24)(19 23)(20 22)

(1 9 19)(2 11 22)(3 12 18)(4 14 20)(5 16 23)(6 10 21)(7 13 24)(8 15 17)

G:=sub<Sym(24)| (1,5)(2,4)(3,7)(6,8)(10,16)(12,14)(17,22)(18,20)(19,24)(21,23), (1,8)(2,7)(3,4)(5,6)(17,24)(18,21)(19,22)(20,23), (1,2)(3,6)(4,5)(7,8)(9,15)(10,16)(11,13)(12,14), (1,2)(3,4)(5,6)(7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24), (1,2)(3,5)(4,6)(7,8)(9,11)(13,15)(17,21)(18,24)(19,23)(20,22), (1,9,19)(2,11,22)(3,12,18)(4,14,20)(5,16,23)(6,10,21)(7,13,24)(8,15,17)>;

G:=Group( (1,5)(2,4)(3,7)(6,8)(10,16)(12,14)(17,22)(18,20)(19,24)(21,23), (1,8)(2,7)(3,4)(5,6)(17,24)(18,21)(19,22)(20,23), (1,2)(3,6)(4,5)(7,8)(9,15)(10,16)(11,13)(12,14), (1,2)(3,4)(5,6)(7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24), (1,2)(3,5)(4,6)(7,8)(9,11)(13,15)(17,21)(18,24)(19,23)(20,22), (1,9,19)(2,11,22)(3,12,18)(4,14,20)(5,16,23)(6,10,21)(7,13,24)(8,15,17) );

G=PermutationGroup([[(1,5),(2,4),(3,7),(6,8),(10,16),(12,14),(17,22),(18,20),(19,24),(21,23)], [(1,8),(2,7),(3,4),(5,6),(17,24),(18,21),(19,22),(20,23)], [(1,2),(3,6),(4,5),(7,8),(9,15),(10,16),(11,13),(12,14)], [(1,2),(3,4),(5,6),(7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24)], [(1,2),(3,5),(4,6),(7,8),(9,11),(13,15),(17,21),(18,24),(19,23),(20,22)], [(1,9,19),(2,11,22),(3,12,18),(4,14,20),(5,16,23),(6,10,21),(7,13,24),(8,15,17)]])

G:=TransitiveGroup(24,500);

Polynomial with Galois group C₂³⋊₂D₄⋊C₃ over ℚ

action	f(x)	Disc(f)
12T104	x¹²-6x¹⁰+12x⁸-8x⁶-3x⁴+6x²-1	-2²⁴·3¹⁶

Matrix representation of C₂³⋊₂D₄⋊C₃ ►in GL₆(ℤ)

-1	0	0	0	0	0
0	-1	0	0	0	0
0	0	0	1	0	0
0	0	1	0	0	0
0	0	0	0	1	0
0	0	0	0	0	-1

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

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	1	0	0	0	0
-1	0	0	0	0	0
0	0	-1	0	0	0
0	0	0	1	0	0
0	0	0	0	0	1
0	0	0	0	1	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	1
0	0	0	0	1	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
1	0	0	0	0	0
0	1	0	0	0	0

G:=sub<GL(6,Integers())| [-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1],[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],[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,-1,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[1,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0] >;

C₂³⋊₂D₄⋊C₃ in GAP, Magma, Sage, TeX

C_2^3\rtimes_2D_4\rtimes C_3

% in TeX

G:=Group("C2^3:2D4:C3");

// GroupNames label

G:=SmallGroup(192,194);

// by ID

G=gap.SmallGroup(192,194);

# by ID

G:=PCGroup([7,-2,-3,-2,2,-2,2,-2,672,1640,135,604,1011,934,521,304,851,1524]);

// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^4=e^2=f^3=1,e*a*e=a*b=b*a,a*c=c*a,d*a*d^-1=a*b*c,f*a*f^-1=e*c=c*e,b*c=c*b,b*d=d*b,b*e=e*b,f*b*f^-1=d^2,c*d=d*c,f*c*f^-1=b,e*d*e=d^-1,f*d*f^-1=a*b*c*d^-1*e,f*e*f^-1=c*d*e>;

// generators/relations

Export

Character table of C₂³⋊₂D₄⋊C₃ in TeX

G = C23⋊2D4⋊C3 order 192 = 26·3

The semidirect product of C23⋊2D4 and C3 acting faithfully

G = C₂³⋊₂D₄⋊C₃ order 192 = 2⁶·3

The semidirect product of C₂³⋊₂D₄ and C₃ acting faithfully