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G = C23⋊F8order 448 = 26·7

2nd semidirect product of C23 and F8 acting via F8/C23=C7

metabelian, soluble, monomial, A-group

Aliases: C263C7, C232F8, SmallGroup(448,1394)

Series: Derived Chief Lower central Upper central

C1C26 — C23⋊F8
C1C23C26 — C23⋊F8
C26 — C23⋊F8
C1

Generators and relations for C23⋊F8
 G = < a,b,c,d,e,f,g | a2=b2=c2=d2=e2=f2=g7=1, ab=ba, gbg-1=ac=ca, ad=da, ae=ea, af=fa, gag-1=c, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, gcg-1=abc, de=ed, df=fd, gdg-1=fe=ef, geg-1=d, gfg-1=e >

Subgroups: 2906 in 411 conjugacy classes, 5 normal (3 characteristic)
C1, C2 [×9], C22 [×93], C7, C23 [×2], C23 [×199], C24 [×93], C25 [×9], F8 [×2], C26, C23⋊F8
Quotients: C1, C7, F8 [×2], C23⋊F8

Character table of C23⋊F8

 class 12A2B2C2D2E2F2G2H2I7A7B7C7D7E7F
 size 1777777777646464646464
ρ11111111111111111    trivial
ρ21111111111ζ73ζ76ζ72ζ75ζ7ζ74    linear of order 7
ρ31111111111ζ75ζ73ζ7ζ76ζ74ζ72    linear of order 7
ρ41111111111ζ72ζ74ζ76ζ7ζ73ζ75    linear of order 7
ρ51111111111ζ74ζ7ζ75ζ72ζ76ζ73    linear of order 7
ρ61111111111ζ7ζ72ζ73ζ74ζ75ζ76    linear of order 7
ρ71111111111ζ76ζ75ζ74ζ73ζ72ζ7    linear of order 7
ρ873-1-1-1-1-53-13000000    orthogonal faithful
ρ973-1-133-1-1-1-5000000    orthogonal faithful
ρ107-1-13-13-1-5-13000000    orthogonal faithful
ρ117-5-133-1-13-1-1000000    orthogonal faithful
ρ127-1-1-1-5333-1-1000000    orthogonal faithful
ρ137-1-1-53-13-1-13000000    orthogonal faithful
ρ147-17-1-1-1-1-1-1-1000000    orthogonal lifted from F8
ρ157-1-1-1-1-1-1-17-1000000    orthogonal lifted from F8
ρ1673-13-1-53-1-1-1000000    orthogonal faithful

Permutation representations of C23⋊F8
On 14 points - transitive group 14T21
Generators in S14
(2 14)(3 8)(4 9)(6 11)
(2 14)(5 10)(6 11)(7 12)
(1 13)(2 14)(3 8)(5 10)
(1 13)(2 14)(3 8)(6 11)
(2 14)(3 8)(4 9)(7 12)
(1 13)(3 8)(4 9)(5 10)
(1 2 3 4 5 6 7)(8 9 10 11 12 13 14)

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

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

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

G:=TransitiveGroup(14,21);

On 28 points - transitive group 28T62
Generators in S28
(2 20)(3 8)(4 9)(5 23)(6 17)(7 25)(10 16)(11 24)(12 18)(14 27)(15 22)(21 28)
(1 26)(2 20)(3 28)(5 16)(6 11)(7 12)(8 21)(10 23)(13 19)(14 27)(17 24)(18 25)
(1 19)(2 14)(3 8)(4 22)(5 16)(6 24)(9 15)(10 23)(11 17)(13 26)(20 27)(21 28)
(1 26)(2 14)(3 28)(4 15)(5 16)(6 11)(8 21)(9 22)(10 23)(13 19)(17 24)(20 27)
(2 27)(3 8)(4 22)(5 16)(6 17)(7 12)(9 15)(10 23)(11 24)(14 20)(18 25)(21 28)
(1 13)(3 28)(4 9)(5 23)(6 17)(7 18)(8 21)(10 16)(11 24)(12 25)(15 22)(19 26)
(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)

G:=sub<Sym(28)| (2,20)(3,8)(4,9)(5,23)(6,17)(7,25)(10,16)(11,24)(12,18)(14,27)(15,22)(21,28), (1,26)(2,20)(3,28)(5,16)(6,11)(7,12)(8,21)(10,23)(13,19)(14,27)(17,24)(18,25), (1,19)(2,14)(3,8)(4,22)(5,16)(6,24)(9,15)(10,23)(11,17)(13,26)(20,27)(21,28), (1,26)(2,14)(3,28)(4,15)(5,16)(6,11)(8,21)(9,22)(10,23)(13,19)(17,24)(20,27), (2,27)(3,8)(4,22)(5,16)(6,17)(7,12)(9,15)(10,23)(11,24)(14,20)(18,25)(21,28), (1,13)(3,28)(4,9)(5,23)(6,17)(7,18)(8,21)(10,16)(11,24)(12,25)(15,22)(19,26), (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)>;

G:=Group( (2,20)(3,8)(4,9)(5,23)(6,17)(7,25)(10,16)(11,24)(12,18)(14,27)(15,22)(21,28), (1,26)(2,20)(3,28)(5,16)(6,11)(7,12)(8,21)(10,23)(13,19)(14,27)(17,24)(18,25), (1,19)(2,14)(3,8)(4,22)(5,16)(6,24)(9,15)(10,23)(11,17)(13,26)(20,27)(21,28), (1,26)(2,14)(3,28)(4,15)(5,16)(6,11)(8,21)(9,22)(10,23)(13,19)(17,24)(20,27), (2,27)(3,8)(4,22)(5,16)(6,17)(7,12)(9,15)(10,23)(11,24)(14,20)(18,25)(21,28), (1,13)(3,28)(4,9)(5,23)(6,17)(7,18)(8,21)(10,16)(11,24)(12,25)(15,22)(19,26), (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) );

G=PermutationGroup([(2,20),(3,8),(4,9),(5,23),(6,17),(7,25),(10,16),(11,24),(12,18),(14,27),(15,22),(21,28)], [(1,26),(2,20),(3,28),(5,16),(6,11),(7,12),(8,21),(10,23),(13,19),(14,27),(17,24),(18,25)], [(1,19),(2,14),(3,8),(4,22),(5,16),(6,24),(9,15),(10,23),(11,17),(13,26),(20,27),(21,28)], [(1,26),(2,14),(3,28),(4,15),(5,16),(6,11),(8,21),(9,22),(10,23),(13,19),(17,24),(20,27)], [(2,27),(3,8),(4,22),(5,16),(6,17),(7,12),(9,15),(10,23),(11,24),(14,20),(18,25),(21,28)], [(1,13),(3,28),(4,9),(5,23),(6,17),(7,18),(8,21),(10,16),(11,24),(12,25),(15,22),(19,26)], [(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)])

G:=TransitiveGroup(28,62);

On 28 points - transitive group 28T63
Generators in S28
(2 19)(3 8)(4 9)(5 24)(6 16)(7 26)(10 15)(11 25)(12 17)(14 28)(20 22)(21 23)
(1 27)(2 19)(3 22)(5 15)(6 11)(7 12)(8 20)(10 24)(13 18)(14 28)(16 25)(17 26)
(1 18)(2 14)(3 8)(4 23)(5 15)(6 25)(9 21)(10 24)(11 16)(13 27)(19 28)(20 22)
(1 27)(2 14)(4 21)(5 10)(6 16)(7 26)(9 23)(11 25)(12 17)(13 18)(15 24)(19 28)
(1 27)(2 28)(3 8)(5 15)(6 11)(7 17)(10 24)(12 26)(13 18)(14 19)(16 25)(20 22)
(1 18)(2 28)(3 22)(4 9)(6 16)(7 12)(8 20)(11 25)(13 27)(14 19)(17 26)(21 23)
(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)

G:=sub<Sym(28)| (2,19)(3,8)(4,9)(5,24)(6,16)(7,26)(10,15)(11,25)(12,17)(14,28)(20,22)(21,23), (1,27)(2,19)(3,22)(5,15)(6,11)(7,12)(8,20)(10,24)(13,18)(14,28)(16,25)(17,26), (1,18)(2,14)(3,8)(4,23)(5,15)(6,25)(9,21)(10,24)(11,16)(13,27)(19,28)(20,22), (1,27)(2,14)(4,21)(5,10)(6,16)(7,26)(9,23)(11,25)(12,17)(13,18)(15,24)(19,28), (1,27)(2,28)(3,8)(5,15)(6,11)(7,17)(10,24)(12,26)(13,18)(14,19)(16,25)(20,22), (1,18)(2,28)(3,22)(4,9)(6,16)(7,12)(8,20)(11,25)(13,27)(14,19)(17,26)(21,23), (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)>;

G:=Group( (2,19)(3,8)(4,9)(5,24)(6,16)(7,26)(10,15)(11,25)(12,17)(14,28)(20,22)(21,23), (1,27)(2,19)(3,22)(5,15)(6,11)(7,12)(8,20)(10,24)(13,18)(14,28)(16,25)(17,26), (1,18)(2,14)(3,8)(4,23)(5,15)(6,25)(9,21)(10,24)(11,16)(13,27)(19,28)(20,22), (1,27)(2,14)(4,21)(5,10)(6,16)(7,26)(9,23)(11,25)(12,17)(13,18)(15,24)(19,28), (1,27)(2,28)(3,8)(5,15)(6,11)(7,17)(10,24)(12,26)(13,18)(14,19)(16,25)(20,22), (1,18)(2,28)(3,22)(4,9)(6,16)(7,12)(8,20)(11,25)(13,27)(14,19)(17,26)(21,23), (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) );

G=PermutationGroup([(2,19),(3,8),(4,9),(5,24),(6,16),(7,26),(10,15),(11,25),(12,17),(14,28),(20,22),(21,23)], [(1,27),(2,19),(3,22),(5,15),(6,11),(7,12),(8,20),(10,24),(13,18),(14,28),(16,25),(17,26)], [(1,18),(2,14),(3,8),(4,23),(5,15),(6,25),(9,21),(10,24),(11,16),(13,27),(19,28),(20,22)], [(1,27),(2,14),(4,21),(5,10),(6,16),(7,26),(9,23),(11,25),(12,17),(13,18),(15,24),(19,28)], [(1,27),(2,28),(3,8),(5,15),(6,11),(7,17),(10,24),(12,26),(13,18),(14,19),(16,25),(20,22)], [(1,18),(2,28),(3,22),(4,9),(6,16),(7,12),(8,20),(11,25),(13,27),(14,19),(17,26),(21,23)], [(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)])

G:=TransitiveGroup(28,63);

On 28 points - transitive group 28T64
Generators in S28
(1 18)(2 19)(3 20)(5 15)(8 22)(10 24)(13 27)(14 28)
(1 18)(4 21)(5 15)(6 16)(9 23)(10 24)(11 25)(13 27)
(1 18)(2 19)(4 21)(7 17)(9 23)(12 26)(13 27)(14 28)
(2 28)(3 8)(4 23)(5 15)(6 16)(7 12)(9 21)(10 24)(11 25)(14 19)(17 26)(20 22)
(1 13)(3 22)(4 9)(5 24)(6 16)(7 17)(8 20)(10 15)(11 25)(12 26)(18 27)(21 23)
(1 18)(2 14)(4 23)(5 10)(6 25)(7 17)(9 21)(11 16)(12 26)(13 27)(15 24)(19 28)
(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)

G:=sub<Sym(28)| (1,18)(2,19)(3,20)(5,15)(8,22)(10,24)(13,27)(14,28), (1,18)(4,21)(5,15)(6,16)(9,23)(10,24)(11,25)(13,27), (1,18)(2,19)(4,21)(7,17)(9,23)(12,26)(13,27)(14,28), (2,28)(3,8)(4,23)(5,15)(6,16)(7,12)(9,21)(10,24)(11,25)(14,19)(17,26)(20,22), (1,13)(3,22)(4,9)(5,24)(6,16)(7,17)(8,20)(10,15)(11,25)(12,26)(18,27)(21,23), (1,18)(2,14)(4,23)(5,10)(6,25)(7,17)(9,21)(11,16)(12,26)(13,27)(15,24)(19,28), (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)>;

G:=Group( (1,18)(2,19)(3,20)(5,15)(8,22)(10,24)(13,27)(14,28), (1,18)(4,21)(5,15)(6,16)(9,23)(10,24)(11,25)(13,27), (1,18)(2,19)(4,21)(7,17)(9,23)(12,26)(13,27)(14,28), (2,28)(3,8)(4,23)(5,15)(6,16)(7,12)(9,21)(10,24)(11,25)(14,19)(17,26)(20,22), (1,13)(3,22)(4,9)(5,24)(6,16)(7,17)(8,20)(10,15)(11,25)(12,26)(18,27)(21,23), (1,18)(2,14)(4,23)(5,10)(6,25)(7,17)(9,21)(11,16)(12,26)(13,27)(15,24)(19,28), (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) );

G=PermutationGroup([(1,18),(2,19),(3,20),(5,15),(8,22),(10,24),(13,27),(14,28)], [(1,18),(4,21),(5,15),(6,16),(9,23),(10,24),(11,25),(13,27)], [(1,18),(2,19),(4,21),(7,17),(9,23),(12,26),(13,27),(14,28)], [(2,28),(3,8),(4,23),(5,15),(6,16),(7,12),(9,21),(10,24),(11,25),(14,19),(17,26),(20,22)], [(1,13),(3,22),(4,9),(5,24),(6,16),(7,17),(8,20),(10,15),(11,25),(12,26),(18,27),(21,23)], [(1,18),(2,14),(4,23),(5,10),(6,25),(7,17),(9,21),(11,16),(12,26),(13,27),(15,24),(19,28)], [(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)])

G:=TransitiveGroup(28,64);

On 28 points - transitive group 28T65
Generators in S28
(2 20)(3 8)(4 9)(5 23)(6 17)(7 25)(10 16)(11 24)(12 18)(14 27)(15 22)(21 28)
(1 26)(2 20)(3 28)(5 16)(6 11)(7 12)(8 21)(10 23)(13 19)(14 27)(17 24)(18 25)
(1 19)(2 14)(3 8)(4 22)(5 16)(6 24)(9 15)(10 23)(11 17)(13 26)(20 27)(21 28)
(1 26)(2 14)(3 8)(4 15)(6 24)(7 18)(9 22)(11 17)(12 25)(13 19)(20 27)(21 28)
(1 19)(2 27)(3 8)(4 9)(5 16)(7 25)(10 23)(12 18)(13 26)(14 20)(15 22)(21 28)
(1 26)(2 20)(3 28)(4 9)(5 10)(6 17)(8 21)(11 24)(13 19)(14 27)(15 22)(16 23)
(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)

G:=sub<Sym(28)| (2,20)(3,8)(4,9)(5,23)(6,17)(7,25)(10,16)(11,24)(12,18)(14,27)(15,22)(21,28), (1,26)(2,20)(3,28)(5,16)(6,11)(7,12)(8,21)(10,23)(13,19)(14,27)(17,24)(18,25), (1,19)(2,14)(3,8)(4,22)(5,16)(6,24)(9,15)(10,23)(11,17)(13,26)(20,27)(21,28), (1,26)(2,14)(3,8)(4,15)(6,24)(7,18)(9,22)(11,17)(12,25)(13,19)(20,27)(21,28), (1,19)(2,27)(3,8)(4,9)(5,16)(7,25)(10,23)(12,18)(13,26)(14,20)(15,22)(21,28), (1,26)(2,20)(3,28)(4,9)(5,10)(6,17)(8,21)(11,24)(13,19)(14,27)(15,22)(16,23), (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)>;

G:=Group( (2,20)(3,8)(4,9)(5,23)(6,17)(7,25)(10,16)(11,24)(12,18)(14,27)(15,22)(21,28), (1,26)(2,20)(3,28)(5,16)(6,11)(7,12)(8,21)(10,23)(13,19)(14,27)(17,24)(18,25), (1,19)(2,14)(3,8)(4,22)(5,16)(6,24)(9,15)(10,23)(11,17)(13,26)(20,27)(21,28), (1,26)(2,14)(3,8)(4,15)(6,24)(7,18)(9,22)(11,17)(12,25)(13,19)(20,27)(21,28), (1,19)(2,27)(3,8)(4,9)(5,16)(7,25)(10,23)(12,18)(13,26)(14,20)(15,22)(21,28), (1,26)(2,20)(3,28)(4,9)(5,10)(6,17)(8,21)(11,24)(13,19)(14,27)(15,22)(16,23), (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) );

G=PermutationGroup([(2,20),(3,8),(4,9),(5,23),(6,17),(7,25),(10,16),(11,24),(12,18),(14,27),(15,22),(21,28)], [(1,26),(2,20),(3,28),(5,16),(6,11),(7,12),(8,21),(10,23),(13,19),(14,27),(17,24),(18,25)], [(1,19),(2,14),(3,8),(4,22),(5,16),(6,24),(9,15),(10,23),(11,17),(13,26),(20,27),(21,28)], [(1,26),(2,14),(3,8),(4,15),(6,24),(7,18),(9,22),(11,17),(12,25),(13,19),(20,27),(21,28)], [(1,19),(2,27),(3,8),(4,9),(5,16),(7,25),(10,23),(12,18),(13,26),(14,20),(15,22),(21,28)], [(1,26),(2,20),(3,28),(4,9),(5,10),(6,17),(8,21),(11,24),(13,19),(14,27),(15,22),(16,23)], [(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)])

G:=TransitiveGroup(28,65);

On 28 points - transitive group 28T66
Generators in S28
(2 19)(3 20)(4 21)(6 16)(8 22)(9 23)(11 25)(14 28)
(2 19)(5 15)(6 16)(7 17)(10 24)(11 25)(12 26)(14 28)
(1 18)(2 19)(3 20)(5 15)(8 22)(10 24)(13 27)(14 28)
(2 28)(3 22)(4 23)(7 26)(8 20)(9 21)(12 17)(14 19)
(1 27)(3 22)(4 23)(5 24)(8 20)(9 21)(10 15)(13 18)
(2 28)(4 23)(5 24)(6 25)(9 21)(10 15)(11 16)(14 19)
(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)

G:=sub<Sym(28)| (2,19)(3,20)(4,21)(6,16)(8,22)(9,23)(11,25)(14,28), (2,19)(5,15)(6,16)(7,17)(10,24)(11,25)(12,26)(14,28), (1,18)(2,19)(3,20)(5,15)(8,22)(10,24)(13,27)(14,28), (2,28)(3,22)(4,23)(7,26)(8,20)(9,21)(12,17)(14,19), (1,27)(3,22)(4,23)(5,24)(8,20)(9,21)(10,15)(13,18), (2,28)(4,23)(5,24)(6,25)(9,21)(10,15)(11,16)(14,19), (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)>;

G:=Group( (2,19)(3,20)(4,21)(6,16)(8,22)(9,23)(11,25)(14,28), (2,19)(5,15)(6,16)(7,17)(10,24)(11,25)(12,26)(14,28), (1,18)(2,19)(3,20)(5,15)(8,22)(10,24)(13,27)(14,28), (2,28)(3,22)(4,23)(7,26)(8,20)(9,21)(12,17)(14,19), (1,27)(3,22)(4,23)(5,24)(8,20)(9,21)(10,15)(13,18), (2,28)(4,23)(5,24)(6,25)(9,21)(10,15)(11,16)(14,19), (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) );

G=PermutationGroup([(2,19),(3,20),(4,21),(6,16),(8,22),(9,23),(11,25),(14,28)], [(2,19),(5,15),(6,16),(7,17),(10,24),(11,25),(12,26),(14,28)], [(1,18),(2,19),(3,20),(5,15),(8,22),(10,24),(13,27),(14,28)], [(2,28),(3,22),(4,23),(7,26),(8,20),(9,21),(12,17),(14,19)], [(1,27),(3,22),(4,23),(5,24),(8,20),(9,21),(10,15),(13,18)], [(2,28),(4,23),(5,24),(6,25),(9,21),(10,15),(11,16),(14,19)], [(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)])

G:=TransitiveGroup(28,66);

Polynomial with Galois group C23⋊F8 over ℚ
actionf(x)Disc(f)
14T21x14-8x12+9x10+75x8-227x6+136x4+112x2-49214·710·4312

Matrix representation of C23⋊F8 in GL7(ℤ)

1000000
0100000
00-10000
000-1000
0000-100
0000010
000000-1
,
1000000
0-100000
00-10000
000-1000
0000100
00000-10
0000001
,
-1000000
0-100000
00-10000
0001000
0000-100
0000010
0000001
,
1000000
0-100000
00-10000
000-1000
0000100
0000010
000000-1
,
1000000
0-100000
0010000
000-1000
0000-100
00000-10
0000001
,
-1000000
0100000
0010000
000-1000
0000100
00000-10
000000-1
,
0000010
0000001
1000000
0100000
0010000
0001000
0000100

G:=sub<GL(7,Integers())| [1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1],[1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1],[-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1],[1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1],[-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1],[0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0] >;

C23⋊F8 in GAP, Magma, Sage, TeX

C_2^3\rtimes F_8
% in TeX

G:=Group("C2^3:F8");
// GroupNames label

G:=SmallGroup(448,1394);
// by ID

G=gap.SmallGroup(448,1394);
# by ID

G:=PCGroup([7,-7,-2,2,2,-2,2,2,491,1031,591,3924,9413,13726]);
// Polycyclic

G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=d^2=e^2=f^2=g^7=1,a*b=b*a,g*b*g^-1=a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,g*a*g^-1=c,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,g*c*g^-1=a*b*c,d*e=e*d,d*f=f*d,g*d*g^-1=f*e=e*f,g*e*g^-1=d,g*f*g^-1=e>;
// generators/relations

Export

Character table of C23⋊F8 in TeX

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