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G = D6≀C2order 288 = 25·32

Wreath product of D6 by C2

non-abelian, soluble, monomial, rational

Aliases: D6C2, C621D4, S322D4, C32⋊C22≀C2, C222S3≀C2, Dic3⋊D61C2, C62⋊C45C2, C6.D61C22, S32⋊C42C2, (C2×C3⋊S3)⋊6D4, (C2×S3≀C2)⋊3C2, (C22×S32)⋊4C2, (C2×S32)⋊1C22, C3⋊S3.6(C2×D4), (C2×C32⋊C4)⋊C22, C2.22(C2×S3≀C2), (C3×C6).22(C2×D4), (C2×C3⋊S3).10C23, (C22×C3⋊S3).52C22, SmallGroup(288,889)

Series: Derived Chief Lower central Upper central

C1C32C2×C3⋊S3 — D6≀C2
C1C32C3⋊S3C2×C3⋊S3C2×S32C2×S3≀C2 — D6≀C2
C32C2×C3⋊S3 — D6≀C2
C1C2C22

Generators and relations for D6≀C2
 G = < a,b,c,d | a6=b6=c4=d2=1, ab=ba, cac-1=a3b, dad=a-1, cbc-1=a2b3, bd=db, dcd=c-1 >

Subgroups: 1336 in 224 conjugacy classes, 29 normal (15 characteristic)
C1, C2, C2 [×9], C3 [×2], C4 [×3], C22, C22 [×23], S3 [×12], C6 [×10], C2×C4 [×3], D4 [×6], C23 [×10], C32, Dic3, C12, D6 [×35], C2×C6 [×9], C22⋊C4 [×3], C2×D4 [×3], C24, C3×S3 [×5], C3⋊S3 [×2], C3⋊S3, C3×C6, C3×C6, C4×S3, D12, C3⋊D4 [×2], C3×D4, C22×S3 [×16], C22×C6, C22≀C2, C3×Dic3, C32⋊C4 [×2], S32 [×4], S32 [×8], S3×C6 [×7], C2×C3⋊S3 [×2], C2×C3⋊S3 [×2], C62, S3×D4, S3×C23, C6.D6, C3⋊D12, C3×C3⋊D4, S3≀C2 [×4], C2×C32⋊C4 [×2], C2×S32, C2×S32 [×2], C2×S32 [×5], S3×C2×C6, C22×C3⋊S3, S32⋊C4 [×2], C62⋊C4, Dic3⋊D6, C2×S3≀C2 [×2], C22×S32, D6≀C2
Quotients: C1, C2 [×7], C22 [×7], D4 [×6], C23, C2×D4 [×3], C22≀C2, S3≀C2, C2×S3≀C2, D6≀C2

Character table of D6≀C2

 class 12A2B2C2D2E2F2G2H2I2J3A3B4A4B4C6A6B6C6D6E6F6G6H6I6J12
 size 11266669912184412363644448121212122424
ρ1111111111111111111111111111    trivial
ρ2111111111-1111-1-1-1111111111-1-1    linear of order 2
ρ311-11-1-11111-111-11-1-1-111-1-11-111-1    linear of order 2
ρ411-11-1-1111-1-1111-11-1-111-1-11-11-11    linear of order 2
ρ5111-1-1-1-111-1111-11111111-1-1-1-1-1-1    linear of order 2
ρ6111-1-1-1-11111111-1-111111-1-1-1-111    linear of order 2
ρ711-1-111-111-1-11111-1-1-111-11-11-1-11    linear of order 2
ρ811-1-111-1111-111-1-11-1-111-11-11-11-1    linear of order 2
ρ92-20-20022-2002200000-2-200-20200    orthogonal lifted from D4
ρ102-20200-22-2002200000-2-20020-200    orthogonal lifted from D4
ρ112220000-2-20-22200022222000000    orthogonal lifted from D4
ρ122-200-220-22002200000-2-2020-2000    orthogonal lifted from D4
ρ1322-20000-2-20222000-2-222-2000000    orthogonal lifted from D4
ρ142-2002-20-22002200000-2-20-202000    orthogonal lifted from D4
ρ154-40-22-2200001-2000-332-1011-1-100    orthogonal faithful
ρ16444222200001-200011-21-2-1-1-1-100    orthogonal lifted from S3≀C2
ρ1744-4-222-200001-2000-1-1-212-11-1100    orthogonal lifted from C2×S3≀C2
ρ184-40-2-22200001-20003-32-10-111-100    orthogonal faithful
ρ1944-400000020-21-200221-2-10000-11    orthogonal lifted from C2×S3≀C2
ρ2044-4000000-20-21200221-2-100001-1    orthogonal lifted from C2×S3≀C2
ρ21444000000-20-21-200-2-21-21000011    orthogonal lifted from S3≀C2
ρ2244400000020-21200-2-21-210000-1-1    orthogonal lifted from S3≀C2
ρ2344-42-2-2200001-2000-1-1-2121-11-100    orthogonal lifted from C2×S3≀C2
ρ244-4022-2-200001-20003-32-101-1-1100    orthogonal faithful
ρ254-402-22-200001-2000-332-10-1-11100    orthogonal faithful
ρ26444-2-2-2-200001-200011-21-2111100    orthogonal lifted from S3≀C2
ρ278-8000000000-4200000-240000000    orthogonal faithful

Permutation representations of D6≀C2
On 12 points - transitive group 12T125
Generators in S12
(1 2)(3 4)(5 6)(7 8 9)(10 11 12)
(1 5 3 2 6 4)(7 12)(8 10)(9 11)
(1 9 3 8)(2 11 4 10)(5 12)(6 7)
(8 9)(10 11)

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

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

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

G:=TransitiveGroup(12,125);

On 24 points - transitive group 24T594
Generators in S24
(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 5 3 4 2 6)(7 10 8 11 9 12)(13 18 17 16 15 14)(19 20 21 22 23 24)
(1 16 4 13)(2 14 6 15)(3 18 5 17)(7 24 12 23)(8 20 11 21)(9 22 10 19)
(1 10)(2 12)(3 11)(4 9)(5 8)(6 7)(13 19)(14 24)(15 23)(16 22)(17 21)(18 20)

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

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

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

G:=TransitiveGroup(24,594);

On 24 points - transitive group 24T655
Generators in S24
(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 16 3 18 5 14)(2 17 4 13 6 15)(7 20 11 24 9 22)(8 21 12 19 10 23)
(1 7 18 24)(2 19 17 12)(3 9 16 22)(4 21 15 10)(5 11 14 20)(6 23 13 8)
(1 24)(2 23)(3 22)(4 21)(5 20)(6 19)(7 18)(8 17)(9 16)(10 15)(11 14)(12 13)

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

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

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

G:=TransitiveGroup(24,655);

On 24 points - transitive group 24T686
Generators in S24
(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 5 7 9 3 12)(2 6 8 10 4 11)(13 19)(14 20)(15 21)(16 22)(17 23)(18 24)
(1 16 9 22)(2 19 10 13)(3 14 12 24)(4 23 11 15)(5 20 7 18)(6 17 8 21)
(1 10)(2 9)(3 6)(4 5)(7 11)(8 12)(13 22)(14 21)(15 20)(16 19)(17 24)(18 23)

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

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

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

G:=TransitiveGroup(24,686);

On 24 points - transitive group 24T687
Generators in S24
(13 14 15 16 17 18)(19 20 21 22 23 24)
(1 5 3 4 2 6)(7 12 8 10 9 11)(13 16)(14 17)(15 18)(19 22)(20 23)(21 24)
(1 13 7 23)(2 17 8 19)(3 15 9 21)(4 16 10 20)(5 14 11 22)(6 18 12 24)
(13 23)(14 22)(15 21)(16 20)(17 19)(18 24)

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

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

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

G:=TransitiveGroup(24,687);

On 24 points - transitive group 24T688
Generators in S24
(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 11 10 5 8 3)(2 12 9 6 7 4)(13 24)(14 19)(15 20)(16 21)(17 22)(18 23)
(1 19 4 24)(2 17 3 16)(5 14 9 13)(6 22 10 21)(7 15 11 18)(8 23 12 20)
(13 14)(15 18)(16 17)(19 24)(20 23)(21 22)

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

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

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

G:=TransitiveGroup(24,688);

On 24 points - transitive group 24T689
Generators in S24
(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 4 9 2 3 10)(5 11 8 6 12 7)(13 24)(14 22)(15 23)(16 21)(17 19)(18 20)
(1 16 7 24)(2 21 8 13)(3 17 11 23)(4 19 12 15)(5 14 10 20)(6 22 9 18)
(1 7)(2 8)(3 6)(4 5)(9 11)(10 12)(14 15)(17 18)(19 20)(22 23)

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

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

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

G:=TransitiveGroup(24,689);

On 24 points - transitive group 24T690
Generators in S24
(13 14 15 16 17 18)(19 20 21 22 23 24)
(1 5 3 4 2 6)(7 8 12 10 9 11)(13 16)(14 17)(15 18)(19 22)(20 23)(21 24)
(1 18)(2 16 3 14)(4 15)(5 13 6 17)(7 24 12 20)(8 19)(9 22)(10 21 11 23)
(1 9)(2 12)(3 7)(4 8)(5 11)(6 10)(13 21)(14 20)(15 19)(16 24)(17 23)(18 22)

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

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

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

G:=TransitiveGroup(24,690);

On 24 points - transitive group 24T691
Generators in S24
(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 12 6 10 4 7)(2 11 5 9 3 8)(13 22)(14 23)(15 24)(16 19)(17 20)(18 21)
(1 20 12 15)(2 14 11 21)(3 18 9 23)(4 24 10 17)(5 16 8 19)(6 22 7 13)
(13 22)(14 21)(15 20)(16 19)(17 24)(18 23)

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

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

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

G:=TransitiveGroup(24,691);

Polynomial with Galois group D6≀C2 over ℚ
actionf(x)Disc(f)
12T125x12-12x10+53x8-107x6+98x4-34x2+2217·176·2932

Matrix representation of D6≀C2 in GL4(ℤ) generated by

1000
0100
0011
00-10
,
1100
-1000
00-10
000-1
,
0010
00-1-1
1000
0100
,
1000
0100
0010
00-1-1
G:=sub<GL(4,Integers())| [1,0,0,0,0,1,0,0,0,0,1,-1,0,0,1,0],[1,-1,0,0,1,0,0,0,0,0,-1,0,0,0,0,-1],[0,0,1,0,0,0,0,1,1,-1,0,0,0,-1,0,0],[1,0,0,0,0,1,0,0,0,0,1,-1,0,0,0,-1] >;

D6≀C2 in GAP, Magma, Sage, TeX

D_6\wr C_2
% in TeX

G:=Group("D6wrC2");
// GroupNames label

G:=SmallGroup(288,889);
// by ID

G=gap.SmallGroup(288,889);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,3,141,219,2693,2028,362,797,1203]);
// Polycyclic

G:=Group<a,b,c,d|a^6=b^6=c^4=d^2=1,a*b=b*a,c*a*c^-1=a^3*b,d*a*d=a^-1,c*b*c^-1=a^2*b^3,b*d=d*b,d*c*d=c^-1>;
// generators/relations

Export

Character table of D6≀C2 in TeX

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