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G = C24.2A4order 192 = 26·3

2nd non-split extension by C24 of A4 acting faithfully

non-abelian, soluble

Aliases: C24.2A4, C23.2SL2(𝔽3), C23.Q8⋊C3, C23.17(C2×A4), C2.C421C6, C23.3A42C2, C2.2(C42⋊C6), C22.3(C2×SL2(𝔽3)), SmallGroup(192,197)

Series: Derived Chief Lower central Upper central

C1C2C2.C42 — C24.2A4
C1C2C23C2.C42C23.3A4 — C24.2A4
C2.C42 — C24.2A4
C1C2

Generators and relations for C24.2A4
 G = < a,b,c,d,e,f,g | a2=b2=c2=d2=g3=1, e2=gbg-1=bcd, f2=gcg-1=b, ab=ba, ac=ca, ad=da, eae-1=abd, faf-1=acd, ag=ga, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, fef-1=de=ed, df=fd, dg=gd, geg-1=bef, gfg-1=cde >

3C2
3C2
4C2
4C2
16C3
3C22
3C22
4C22
6C22
6C4
6C4
6C22
12C4
12C22
16C6
16C6
16C6
3C2×C4
3C2×C4
6C23
6C2×C4
6C23
6C2×C4
6C2×C4
6C2×C4
6C2×C4
4A4
16C2×C6
3C22×C4
3C22×C4
6C4⋊C4
6C22⋊C4
6C4⋊C4
6C22⋊C4
4C2×A4
4C2×A4
4C2×A4
3C2×C22⋊C4
3C2×C4⋊C4
4C22×A4

Character table of C24.2A4

 class 12A2B2C2D2E3A3B4A4B4C4D6A6B6C6D6E6F
 size 113344161612121212161616161616
ρ1111111111111111111    trivial
ρ21111-1-11111-1-1-11-1-1-11    linear of order 2
ρ3111111ζ3ζ321111ζ32ζ32ζ3ζ3ζ32ζ3    linear of order 3
ρ41111-1-1ζ32ζ311-1-1ζ65ζ3ζ6ζ6ζ65ζ32    linear of order 6
ρ5111111ζ32ζ31111ζ3ζ3ζ32ζ32ζ3ζ32    linear of order 3
ρ61111-1-1ζ3ζ3211-1-1ζ6ζ32ζ65ζ65ζ6ζ3    linear of order 6
ρ72-22-22-2-1-10000-111-111    symplectic lifted from SL2(𝔽3), Schur index 2
ρ82-22-2-22-1-1000011-11-11    symplectic lifted from SL2(𝔽3), Schur index 2
ρ92-22-2-22ζ6ζ650000ζ3ζ3ζ6ζ32ζ65ζ32    complex lifted from SL2(𝔽3)
ρ102-22-2-22ζ65ζ60000ζ32ζ32ζ65ζ3ζ6ζ3    complex lifted from SL2(𝔽3)
ρ112-22-22-2ζ6ζ650000ζ65ζ3ζ32ζ6ζ3ζ32    complex lifted from SL2(𝔽3)
ρ122-22-22-2ζ65ζ60000ζ6ζ32ζ3ζ65ζ32ζ3    complex lifted from SL2(𝔽3)
ρ133333-3-300-1-111000000    orthogonal lifted from C2×A4
ρ1433333300-1-1-1-1000000    orthogonal lifted from A4
ρ156-6-220000002-2000000    orthogonal faithful
ρ166-6-22000000-22000000    orthogonal faithful
ρ1766-2-200002i-2i00000000    complex lifted from C42⋊C6
ρ1866-2-20000-2i2i00000000    complex lifted from C42⋊C6

Permutation representations of C24.2A4
On 12 points - transitive group 12T91
Generators in S12
(1 8)(2 7)(3 4)(5 6)(9 12)(10 11)
(3 5)(4 6)
(1 2)(7 8)
(1 2)(3 5)(4 6)(7 8)(9 11)(10 12)
(3 4)(5 6)(7 8)(9 10 11 12)
(1 7)(2 8)(3 6 5 4)(10 12)
(1 9 4)(2 11 6)(3 8 12)(5 7 10)

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

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

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

G:=TransitiveGroup(12,91);

On 12 points - transitive group 12T93
Generators in S12
(3 4)(5 7)(10 12)
(1 2)(3 4)
(5 7)(6 8)
(1 2)(3 4)(5 7)(6 8)(9 11)(10 12)
(3 4)(5 6)(7 8)(9 10 11 12)
(1 4 2 3)(6 8)(9 10)(11 12)
(1 6 11)(2 8 9)(3 5 12)(4 7 10)

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

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

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

G:=TransitiveGroup(12,93);

On 24 points - transitive group 24T460
Generators in S24
(1 10)(2 9)(3 7)(4 8)(5 12)(6 11)(13 16)(14 15)(17 22)(18 21)(19 24)(20 23)
(5 15)(6 16)(11 13)(12 14)
(1 2)(3 4)(7 8)(9 10)
(1 2)(3 4)(5 15)(6 16)(7 8)(9 10)(11 13)(12 14)(17 19)(18 20)(21 23)(22 24)
(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)(17 18 19 20)(21 22 23 24)
(1 7)(2 8)(3 10)(4 9)(5 6 15 16)(11 12 13 14)(17 19)(21 23)
(1 24 5)(2 22 15)(3 18 13)(4 20 11)(6 8 23)(7 21 16)(9 17 14)(10 19 12)

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

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

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

G:=TransitiveGroup(24,460);

On 24 points - transitive group 24T461
Generators in S24
(1 2)(3 4)(5 6)(7 8)(9 13)(10 15)(11 14)(12 16)(17 22)(18 21)(19 24)(20 23)
(1 4)(2 3)(5 7)(6 8)
(9 12)(10 11)(13 16)(14 15)
(1 4)(2 3)(5 7)(6 8)(9 12)(10 11)(13 16)(14 15)(17 19)(18 20)(21 23)(22 24)
(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 7 4 5)(2 6 3 8)(9 16)(10 14)(11 15)(12 13)(17 23)(18 22)(19 21)(20 24)
(1 12 18)(2 16 21)(3 13 23)(4 9 20)(5 15 19)(6 10 24)(7 14 17)(8 11 22)

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

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

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

G:=TransitiveGroup(24,461);

On 24 points - transitive group 24T462
Generators in S24
(1 3)(2 4)(5 10)(6 15)(7 11)(8 12)(9 13)(14 16)(17 18)(19 20)(21 22)(23 24)
(1 12)(2 11)(3 8)(4 7)
(5 14)(6 13)(9 15)(10 16)
(1 12)(2 11)(3 8)(4 7)(5 14)(6 13)(9 15)(10 16)(17 19)(18 20)(21 23)(22 24)
(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 3 12 8)(2 7 11 4)(5 9)(6 16)(10 13)(14 15)(17 23)(18 22)(19 21)(20 24)
(1 6 24)(2 10 19)(3 15 23)(4 5 20)(7 14 18)(8 9 21)(11 16 17)(12 13 22)

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

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

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

G:=TransitiveGroup(24,462);

On 24 points - transitive group 24T467
Generators in S24
(1 6)(2 5)(10 12)(14 15)(18 20)(21 23)
(1 6)(2 5)(3 7)(4 8)
(9 11)(10 12)(13 16)(14 15)
(1 6)(2 5)(3 7)(4 8)(9 11)(10 12)(13 16)(14 15)(17 19)(18 20)(21 23)(22 24)
(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 3 6 7)(2 8 5 4)(9 13)(10 15)(11 16)(12 14)(17 23)(18 22)(19 21)(20 24)
(1 14 23)(2 10 20)(3 11 22)(4 13 17)(5 12 18)(6 15 21)(7 9 24)(8 16 19)

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

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

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

G:=TransitiveGroup(24,467);

On 24 points - transitive group 24T468
Generators in S24
(1 4)(2 3)(5 10)(6 13)(7 14)(8 9)(11 16)(12 15)(17 23)(18 22)(19 21)(20 24)
(1 3)(2 4)(11 12)(15 16)
(5 7)(6 8)(9 13)(10 14)
(1 3)(2 4)(5 7)(6 8)(9 13)(10 14)(11 12)(15 16)(17 19)(18 20)(21 23)(22 24)
(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)(17 18 19 20)(21 22 23 24)
(1 12 3 11)(2 15 4 16)(6 8)(9 13)(17 18)(19 20)(21 22)(23 24)
(1 8 23)(2 13 19)(3 6 21)(4 9 17)(5 22 12)(7 24 11)(10 18 15)(14 20 16)

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

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

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

G:=TransitiveGroup(24,468);

Polynomial with Galois group C24.2A4 over ℚ
actionf(x)Disc(f)
12T91x12-534x10+78489x8-4839186x6+143348046x4-2021896020x2+10884540241236·316·1730·1930·4235574
12T93x12-30x10+327x8-1566x6+3096x4-1938x2+323224·320·712·175·195

Matrix representation of C24.2A4 in GL6(ℤ)

010000
100000
000100
001000
000001
000010
,
100000
010000
00-1000
000-100
000010
000001
,
-100000
0-10000
001000
000100
000010
000001
,
-100000
0-10000
00-1000
000-100
0000-10
00000-1
,
100000
0-10000
000-100
00-1000
00000-1
000010
,
010000
100000
000100
00-1000
000010
00000-1
,
001000
000100
000010
000001
100000
010000

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

C24.2A4 in GAP, Magma, Sage, TeX

C_2^4._2A_4
% in TeX

G:=Group("C2^4.2A4");
// GroupNames label

G:=SmallGroup(192,197);
// by ID

G=gap.SmallGroup(192,197);
# by ID

G:=PCGroup([7,-2,-3,-2,2,-2,2,-2,632,135,268,4371,934,521,304,2531,1524]);
// Polycyclic

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

Export

Subgroup lattice of C24.2A4 in TeX
Character table of C24.2A4 in TeX

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