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G = C24⋊C23order 128 = 27

2nd semidirect product of C24 and C23 acting faithfully

p-group, metabelian, nilpotent (class 3), monomial, rational

Aliases: C245D4, C242C23, C23.8C24, 2+ 1+4.14C22, (C2×D4)⋊26D4, (C22×C4)⋊7D4, C2≀C224C2, C233D43C2, C23⋊C48C22, C22⋊C43C23, (C22×C4)⋊2C23, C23.27(C2×D4), C22≀C21C22, C22.6C22≀C2, (C2×D4).42C23, C23.7D44C2, (C22×D4)⋊21C22, (C2×2+ 1+4)⋊6C2, C22.42(C22×D4), C22.D41C22, (C2×C4).28(C2×D4), (C2×C23⋊C4)⋊18C2, C2.63(C2×C22≀C2), (C2×C22⋊C4)⋊38C22, SmallGroup(128,1758)

Series: Derived Chief Lower central Upper central Jennings

C1C23 — C24⋊C23
C1C2C22C23C24C22×D4C2×2+ 1+4 — C24⋊C23
C1C2C23 — C24⋊C23
C1C2C24 — C24⋊C23
C1C2C23 — C24⋊C23

Generators and relations for C24⋊C23
 G = < a,b,c,d,e,f,g | a2=b2=c2=d2=e2=f2=g2=1, eae=ab=ba, faf=ac=ca, gag=ad=da, bc=cb, fbf=bd=db, be=eb, bg=gb, ece=cd=dc, cf=fc, cg=gc, de=ed, df=fd, dg=gd, ef=fe, eg=ge, fg=gf >

Subgroups: 924 in 400 conjugacy classes, 106 normal (10 characteristic)
C1, C2, C2 [×14], C4 [×13], C22, C22 [×6], C22 [×39], C2×C4 [×6], C2×C4 [×30], D4 [×46], Q8 [×4], C23, C23 [×12], C23 [×20], C22⋊C4 [×6], C22⋊C4 [×15], C4⋊C4 [×6], C22×C4, C22×C4 [×3], C22×C4 [×6], C2×D4 [×12], C2×D4 [×51], C2×Q8, C4○D4 [×24], C24 [×2], C24 [×3], C24, C23⋊C4 [×12], C2×C22⋊C4 [×3], C22≀C2 [×6], C22≀C2 [×3], C4⋊D4 [×6], C22.D4 [×6], C22.D4 [×3], C22×D4, C22×D4 [×3], C22×D4 [×3], C2×C4○D4 [×3], 2+ 1+4 [×4], 2+ 1+4 [×6], C2×C23⋊C4 [×3], C2≀C22 [×4], C23.7D4 [×4], C233D4 [×3], C2×2+ 1+4, C24⋊C23
Quotients: C1, C2 [×15], C22 [×35], D4 [×12], C23 [×15], C2×D4 [×18], C24, C22≀C2 [×4], C22×D4 [×3], C2×C22≀C2, C24⋊C23

Character table of C24⋊C23

 class 12A2B2C2D2E2F2G2H2I2J2K2L2M2N2O4A4B4C4D4E4F4G4H4I4J4K4L4M
 size 11222222244444484444448888888
ρ111111111111111111111111111111    trivial
ρ211-1111-1-1-111-11-1-1111-1-11-111-1-11-1-1    linear of order 2
ρ311-1111-1-1-11-11-1-11-1-11-11-111-11-111-1    linear of order 2
ρ41111111111-1-1-11-1-1-111-1-1-11-1-111-11    linear of order 2
ρ5111111111-11-1-1-111-1-1-111-1-1-1-1111-1    linear of order 2
ρ611-1111-1-1-1-111-11-11-1-11-111-1-11-11-11    linear of order 2
ρ711-1111-1-1-1-1-1-1111-11-111-1-1-11-1-1111    linear of order 2
ρ8111111111-1-111-1-1-11-1-1-1-11-11111-1-1    linear of order 2
ρ9111111111111111-1111111-1-1-1-1-1-1-1    linear of order 2
ρ1011-1111-1-1-111-11-1-1-111-1-11-1-1-111-111    linear of order 2
ρ1111-1111-1-1-11-11-1-111-11-11-11-11-11-1-11    linear of order 2
ρ121111111111-1-1-11-11-111-1-1-1-111-1-11-1    linear of order 2
ρ13111111111-11-1-1-11-1-1-1-111-1111-1-1-11    linear of order 2
ρ1411-1111-1-1-1-111-11-1-1-1-11-11111-11-11-1    linear of order 2
ρ1511-1111-1-1-1-1-1-111111-111-1-11-111-1-1-1    linear of order 2
ρ16111111111-1-111-1-111-1-1-1-111-1-1-1-111    linear of order 2
ρ1722-2-2-2222-2002-200020000-20000000    orthogonal lifted from D4
ρ1822-2-2-2222-200-22000-2000020000000    orthogonal lifted from D4
ρ19222-22-2-22-20200020000-2-200000000    orthogonal lifted from D4
ρ2022-22-2-2-222-200020002-20000000000    orthogonal lifted from D4
ρ21222-22-2-22-20-2000-200002200000000    orthogonal lifted from D4
ρ222222-2-22-2-2-2000-2000220000000000    orthogonal lifted from D4
ρ23222-2-22-2-220022000-20000-20000000    orthogonal lifted from D4
ρ24222-2-22-2-2200-2-20002000020000000    orthogonal lifted from D4
ρ252222-2-22-2-220002000-2-20000000000    orthogonal lifted from D4
ρ2622-2-22-22-2202000-200002-200000000    orthogonal lifted from D4
ρ2722-2-22-22-220-200020000-2200000000    orthogonal lifted from D4
ρ2822-22-2-2-2222000-2000-220000000000    orthogonal lifted from D4
ρ298-8000000000000000000000000000    orthogonal faithful

Permutation representations of C24⋊C23
On 16 points - transitive group 16T241
Generators in S16
(1 2)(3 4)(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)
(3 10)(4 9)(7 11)(8 12)
(3 10)(4 9)(5 15)(6 16)
(1 13)(2 14)(3 10)(4 9)(5 15)(6 16)(7 11)(8 12)
(1 5)(2 6)(3 11)(4 8)(7 10)(9 12)(13 15)(14 16)
(1 11)(2 12)(3 5)(4 16)(6 9)(7 13)(8 14)(10 15)
(2 14)(4 9)(6 16)(8 12)

G:=sub<Sym(16)| (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (3,10)(4,9)(7,11)(8,12), (3,10)(4,9)(5,15)(6,16), (1,13)(2,14)(3,10)(4,9)(5,15)(6,16)(7,11)(8,12), (1,5)(2,6)(3,11)(4,8)(7,10)(9,12)(13,15)(14,16), (1,11)(2,12)(3,5)(4,16)(6,9)(7,13)(8,14)(10,15), (2,14)(4,9)(6,16)(8,12)>;

G:=Group( (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (3,10)(4,9)(7,11)(8,12), (3,10)(4,9)(5,15)(6,16), (1,13)(2,14)(3,10)(4,9)(5,15)(6,16)(7,11)(8,12), (1,5)(2,6)(3,11)(4,8)(7,10)(9,12)(13,15)(14,16), (1,11)(2,12)(3,5)(4,16)(6,9)(7,13)(8,14)(10,15), (2,14)(4,9)(6,16)(8,12) );

G=PermutationGroup([(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)], [(3,10),(4,9),(7,11),(8,12)], [(3,10),(4,9),(5,15),(6,16)], [(1,13),(2,14),(3,10),(4,9),(5,15),(6,16),(7,11),(8,12)], [(1,5),(2,6),(3,11),(4,8),(7,10),(9,12),(13,15),(14,16)], [(1,11),(2,12),(3,5),(4,16),(6,9),(7,13),(8,14),(10,15)], [(2,14),(4,9),(6,16),(8,12)])

G:=TransitiveGroup(16,241);

On 16 points - transitive group 16T277
Generators in S16
(1 2)(3 4)(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)
(1 15)(2 16)(3 13)(4 14)(5 10)(6 9)(7 12)(8 11)
(1 6)(2 5)(3 7)(4 8)(9 15)(10 16)(11 14)(12 13)
(1 11)(2 12)(3 10)(4 9)(5 13)(6 14)(7 16)(8 15)
(1 15)(3 10)(4 6)(5 13)(8 11)(9 14)
(1 6)(3 10)(4 15)(7 16)(8 9)(11 14)
(2 12)(3 10)(5 13)(7 16)

G:=sub<Sym(16)| (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (1,15)(2,16)(3,13)(4,14)(5,10)(6,9)(7,12)(8,11), (1,6)(2,5)(3,7)(4,8)(9,15)(10,16)(11,14)(12,13), (1,11)(2,12)(3,10)(4,9)(5,13)(6,14)(7,16)(8,15), (1,15)(3,10)(4,6)(5,13)(8,11)(9,14), (1,6)(3,10)(4,15)(7,16)(8,9)(11,14), (2,12)(3,10)(5,13)(7,16)>;

G:=Group( (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (1,15)(2,16)(3,13)(4,14)(5,10)(6,9)(7,12)(8,11), (1,6)(2,5)(3,7)(4,8)(9,15)(10,16)(11,14)(12,13), (1,11)(2,12)(3,10)(4,9)(5,13)(6,14)(7,16)(8,15), (1,15)(3,10)(4,6)(5,13)(8,11)(9,14), (1,6)(3,10)(4,15)(7,16)(8,9)(11,14), (2,12)(3,10)(5,13)(7,16) );

G=PermutationGroup([(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)], [(1,15),(2,16),(3,13),(4,14),(5,10),(6,9),(7,12),(8,11)], [(1,6),(2,5),(3,7),(4,8),(9,15),(10,16),(11,14),(12,13)], [(1,11),(2,12),(3,10),(4,9),(5,13),(6,14),(7,16),(8,15)], [(1,15),(3,10),(4,6),(5,13),(8,11),(9,14)], [(1,6),(3,10),(4,15),(7,16),(8,9),(11,14)], [(2,12),(3,10),(5,13),(7,16)])

G:=TransitiveGroup(16,277);

On 16 points - transitive group 16T301
Generators in S16
(9 10)(11 12)(13 14)(15 16)
(3 5)(4 8)(11 12)(15 16)
(4 8)(6 7)(9 10)(15 16)
(1 2)(3 5)(4 8)(6 7)(9 10)(11 12)(13 14)(15 16)
(1 6)(2 7)(3 16)(4 12)(5 15)(8 11)(9 14)(10 13)
(1 5)(2 3)(4 10)(6 15)(7 16)(8 9)(11 14)(12 13)
(1 14)(2 13)(3 12)(4 16)(5 11)(6 9)(7 10)(8 15)

G:=sub<Sym(16)| (9,10)(11,12)(13,14)(15,16), (3,5)(4,8)(11,12)(15,16), (4,8)(6,7)(9,10)(15,16), (1,2)(3,5)(4,8)(6,7)(9,10)(11,12)(13,14)(15,16), (1,6)(2,7)(3,16)(4,12)(5,15)(8,11)(9,14)(10,13), (1,5)(2,3)(4,10)(6,15)(7,16)(8,9)(11,14)(12,13), (1,14)(2,13)(3,12)(4,16)(5,11)(6,9)(7,10)(8,15)>;

G:=Group( (9,10)(11,12)(13,14)(15,16), (3,5)(4,8)(11,12)(15,16), (4,8)(6,7)(9,10)(15,16), (1,2)(3,5)(4,8)(6,7)(9,10)(11,12)(13,14)(15,16), (1,6)(2,7)(3,16)(4,12)(5,15)(8,11)(9,14)(10,13), (1,5)(2,3)(4,10)(6,15)(7,16)(8,9)(11,14)(12,13), (1,14)(2,13)(3,12)(4,16)(5,11)(6,9)(7,10)(8,15) );

G=PermutationGroup([(9,10),(11,12),(13,14),(15,16)], [(3,5),(4,8),(11,12),(15,16)], [(4,8),(6,7),(9,10),(15,16)], [(1,2),(3,5),(4,8),(6,7),(9,10),(11,12),(13,14),(15,16)], [(1,6),(2,7),(3,16),(4,12),(5,15),(8,11),(9,14),(10,13)], [(1,5),(2,3),(4,10),(6,15),(7,16),(8,9),(11,14),(12,13)], [(1,14),(2,13),(3,12),(4,16),(5,11),(6,9),(7,10),(8,15)])

G:=TransitiveGroup(16,301);

On 16 points - transitive group 16T309
Generators in S16
(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)
(5 8)(6 7)(11 15)(12 16)
(1 4)(2 3)(5 6)(7 8)(9 13)(10 14)(11 16)(12 15)
(1 2)(3 4)(5 8)(6 7)(9 10)(11 15)(12 16)(13 14)
(3 4)(6 7)(11 15)(13 14)
(1 5)(2 8)(3 7)(4 6)(9 16)(10 12)(11 13)(14 15)
(1 10)(2 9)(3 13)(4 14)(5 12)(6 15)(7 11)(8 16)

G:=sub<Sym(16)| (5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (5,8)(6,7)(11,15)(12,16), (1,4)(2,3)(5,6)(7,8)(9,13)(10,14)(11,16)(12,15), (1,2)(3,4)(5,8)(6,7)(9,10)(11,15)(12,16)(13,14), (3,4)(6,7)(11,15)(13,14), (1,5)(2,8)(3,7)(4,6)(9,16)(10,12)(11,13)(14,15), (1,10)(2,9)(3,13)(4,14)(5,12)(6,15)(7,11)(8,16)>;

G:=Group( (5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (5,8)(6,7)(11,15)(12,16), (1,4)(2,3)(5,6)(7,8)(9,13)(10,14)(11,16)(12,15), (1,2)(3,4)(5,8)(6,7)(9,10)(11,15)(12,16)(13,14), (3,4)(6,7)(11,15)(13,14), (1,5)(2,8)(3,7)(4,6)(9,16)(10,12)(11,13)(14,15), (1,10)(2,9)(3,13)(4,14)(5,12)(6,15)(7,11)(8,16) );

G=PermutationGroup([(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)], [(5,8),(6,7),(11,15),(12,16)], [(1,4),(2,3),(5,6),(7,8),(9,13),(10,14),(11,16),(12,15)], [(1,2),(3,4),(5,8),(6,7),(9,10),(11,15),(12,16),(13,14)], [(3,4),(6,7),(11,15),(13,14)], [(1,5),(2,8),(3,7),(4,6),(9,16),(10,12),(11,13),(14,15)], [(1,10),(2,9),(3,13),(4,14),(5,12),(6,15),(7,11),(8,16)])

G:=TransitiveGroup(16,309);

On 16 points - transitive group 16T320
Generators in S16
(1 2)(3 4)(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)
(1 14)(2 13)(3 6)(4 5)(7 16)(8 15)(9 11)(10 12)
(1 6)(2 5)(3 14)(4 13)(7 16)(8 15)(9 11)(10 12)
(1 3)(2 4)(5 13)(6 14)(7 9)(8 10)(11 16)(12 15)
(1 16)(2 8)(3 11)(4 10)(5 12)(6 9)(7 14)(13 15)
(1 8)(2 16)(3 10)(4 11)(5 7)(6 15)(9 13)(12 14)
(1 14)(2 5)(3 6)(4 13)(7 16)(8 12)(9 11)(10 15)

G:=sub<Sym(16)| (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (1,14)(2,13)(3,6)(4,5)(7,16)(8,15)(9,11)(10,12), (1,6)(2,5)(3,14)(4,13)(7,16)(8,15)(9,11)(10,12), (1,3)(2,4)(5,13)(6,14)(7,9)(8,10)(11,16)(12,15), (1,16)(2,8)(3,11)(4,10)(5,12)(6,9)(7,14)(13,15), (1,8)(2,16)(3,10)(4,11)(5,7)(6,15)(9,13)(12,14), (1,14)(2,5)(3,6)(4,13)(7,16)(8,12)(9,11)(10,15)>;

G:=Group( (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (1,14)(2,13)(3,6)(4,5)(7,16)(8,15)(9,11)(10,12), (1,6)(2,5)(3,14)(4,13)(7,16)(8,15)(9,11)(10,12), (1,3)(2,4)(5,13)(6,14)(7,9)(8,10)(11,16)(12,15), (1,16)(2,8)(3,11)(4,10)(5,12)(6,9)(7,14)(13,15), (1,8)(2,16)(3,10)(4,11)(5,7)(6,15)(9,13)(12,14), (1,14)(2,5)(3,6)(4,13)(7,16)(8,12)(9,11)(10,15) );

G=PermutationGroup([(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)], [(1,14),(2,13),(3,6),(4,5),(7,16),(8,15),(9,11),(10,12)], [(1,6),(2,5),(3,14),(4,13),(7,16),(8,15),(9,11),(10,12)], [(1,3),(2,4),(5,13),(6,14),(7,9),(8,10),(11,16),(12,15)], [(1,16),(2,8),(3,11),(4,10),(5,12),(6,9),(7,14),(13,15)], [(1,8),(2,16),(3,10),(4,11),(5,7),(6,15),(9,13),(12,14)], [(1,14),(2,5),(3,6),(4,13),(7,16),(8,12),(9,11),(10,15)])

G:=TransitiveGroup(16,320);

On 16 points - transitive group 16T329
Generators in S16
(1 2)(3 4)(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)
(1 7)(2 8)(3 16)(4 15)(5 9)(6 10)(11 13)(12 14)
(1 7)(2 8)(3 11)(4 12)(5 9)(6 10)(13 16)(14 15)
(1 10)(2 9)(3 13)(4 14)(5 8)(6 7)(11 16)(12 15)
(1 16)(2 4)(3 7)(5 12)(6 13)(8 15)(9 14)(10 11)
(1 11)(2 4)(3 7)(5 15)(6 13)(8 12)(9 14)(10 16)
(1 10)(3 13)(6 7)(11 16)

G:=sub<Sym(16)| (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (1,7)(2,8)(3,16)(4,15)(5,9)(6,10)(11,13)(12,14), (1,7)(2,8)(3,11)(4,12)(5,9)(6,10)(13,16)(14,15), (1,10)(2,9)(3,13)(4,14)(5,8)(6,7)(11,16)(12,15), (1,16)(2,4)(3,7)(5,12)(6,13)(8,15)(9,14)(10,11), (1,11)(2,4)(3,7)(5,15)(6,13)(8,12)(9,14)(10,16), (1,10)(3,13)(6,7)(11,16)>;

G:=Group( (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (1,7)(2,8)(3,16)(4,15)(5,9)(6,10)(11,13)(12,14), (1,7)(2,8)(3,11)(4,12)(5,9)(6,10)(13,16)(14,15), (1,10)(2,9)(3,13)(4,14)(5,8)(6,7)(11,16)(12,15), (1,16)(2,4)(3,7)(5,12)(6,13)(8,15)(9,14)(10,11), (1,11)(2,4)(3,7)(5,15)(6,13)(8,12)(9,14)(10,16), (1,10)(3,13)(6,7)(11,16) );

G=PermutationGroup([(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)], [(1,7),(2,8),(3,16),(4,15),(5,9),(6,10),(11,13),(12,14)], [(1,7),(2,8),(3,11),(4,12),(5,9),(6,10),(13,16),(14,15)], [(1,10),(2,9),(3,13),(4,14),(5,8),(6,7),(11,16),(12,15)], [(1,16),(2,4),(3,7),(5,12),(6,13),(8,15),(9,14),(10,11)], [(1,11),(2,4),(3,7),(5,15),(6,13),(8,12),(9,14),(10,16)], [(1,10),(3,13),(6,7),(11,16)])

G:=TransitiveGroup(16,329);

Matrix representation of C24⋊C23 in GL8(ℤ)

00001000
00000100
00000010
00000001
10000000
01000000
00100000
00010000
,
00100000
00010000
10000000
01000000
00000010
00000001
00001000
00000100
,
01000000
10000000
00010000
00100000
00000100
00001000
00000001
00000010
,
-10000000
0-1000000
00-100000
000-10000
0000-1000
00000-100
000000-10
0000000-1
,
10000000
0-1000000
00100000
000-10000
00000010
0000000-1
00001000
00000-100
,
10000000
01000000
00-100000
000-10000
00000100
00001000
0000000-1
000000-10
,
10000000
01000000
00100000
00010000
0000-1000
00000-100
000000-10
0000000-1

G:=sub<GL(8,Integers())| [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],[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,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0],[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],[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] >;

C24⋊C23 in GAP, Magma, Sage, TeX

C_2^4\rtimes C_2^3
% in TeX

G:=Group("C2^4:C2^3");
// GroupNames label

G:=SmallGroup(128,1758);
// by ID

G=gap.SmallGroup(128,1758);
# by ID

G:=PCGroup([7,-2,2,2,2,-2,2,-2,253,758,2019,718,2028]);
// Polycyclic

G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=d^2=e^2=f^2=g^2=1,e*a*e=a*b=b*a,f*a*f=a*c=c*a,g*a*g=a*d=d*a,b*c=c*b,f*b*f=b*d=d*b,b*e=e*b,b*g=g*b,e*c*e=c*d=d*c,c*f=f*c,c*g=g*c,d*e=e*d,d*f=f*d,d*g=g*d,e*f=f*e,e*g=g*e,f*g=g*f>;
// generators/relations

Export

Character table of C24⋊C23 in TeX

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