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G = C24.28D4order 128 = 27

28th non-split extension by C24 of D4 acting faithfully

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

Aliases: C24.28D4, C24.2C23, C242(C2×C4), C22≀C21C4, C22⋊C431D4, (C2×D4).82D4, C22.11(C4×D4), (C22×C4).70D4, C22.D41C4, C23.136(C2×D4), C233D4.4C2, C22.11C245C2, C22.36C22≀C2, C23.9D410C2, C22.4(C4⋊D4), C23.70(C22×C4), C23.124(C4○D4), C23.16(C22⋊C4), (C22×D4).34C22, C2.52(C23.23D4), C22.11(C22.D4), (C2×C23⋊C4)⋊6C2, C22⋊C47(C2×C4), (C22×C4)⋊2(C2×C4), (C2×D4).91(C2×C4), (C2×C4).20(C22⋊C4), C22.51(C2×C22⋊C4), (C2×C22⋊C4).14C22, SmallGroup(128,645)

Series: Derived Chief Lower central Upper central Jennings

C1C23 — C24.28D4
C1C2C22C23C24C22×D4C22.11C24 — C24.28D4
C1C2C23 — C24.28D4
C1C2C24 — C24.28D4
C1C2C24 — C24.28D4

Generators and relations for C24.28D4
 G = < a,b,c,d,e,f | a2=b2=c2=d2=e4=1, f2=d, ab=ba, ac=ca, ad=da, eae-1=faf-1=acd, bc=cb, ebe-1=fbf-1=bd=db, ece-1=cd=dc, cf=fc, de=ed, df=fd, fef-1=bde-1 >

Subgroups: 492 in 190 conjugacy classes, 54 normal (20 characteristic)
C1, C2, C2 [×10], C4 [×11], C22 [×3], C22 [×4], C22 [×19], C2×C4 [×2], C2×C4 [×20], D4 [×14], C23 [×3], C23 [×6], C23 [×8], C42 [×2], C22⋊C4 [×6], C22⋊C4 [×13], C4⋊C4 [×4], C22×C4 [×2], C22×C4 [×7], C2×D4 [×4], C2×D4 [×12], C24 [×3], C23⋊C4 [×6], C2×C22⋊C4, C2×C22⋊C4 [×4], C2×C22⋊C4, C42⋊C2, C4×D4 [×4], C22≀C2 [×2], C22≀C2, C4⋊D4 [×2], C22.D4 [×2], C22.D4, C22×D4 [×2], C23.9D4 [×2], C2×C23⋊C4, C2×C23⋊C4 [×2], C22.11C24, C233D4, C24.28D4
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×8], C23, C22⋊C4 [×4], C22×C4, C2×D4 [×4], C4○D4 [×2], C2×C22⋊C4, C4×D4 [×2], C22≀C2, C4⋊D4 [×2], C22.D4, C23.23D4, C24.28D4

Character table of C24.28D4

 class 12A2B2C2D2E2F2G2H2I2J2K4A4B4C4D4E4F4G4H4I4J4K4L4M4N4O4P4Q
 size 11222222244844444444448888888
ρ111111111111111111111111111111    trivial
ρ21111111111111-1-1-1-1-1-1-1-1111-1-1-11-1    linear of order 2
ρ3111111111-1-11-1-1111-1-1-11-11-11-11-1-1    linear of order 2
ρ4111111111-1-11-11-1-1-1111-1-11-1-11-1-11    linear of order 2
ρ511111111111-11111111111-1-1-1-1-1-1-1    linear of order 2
ρ611111111111-11-1-1-1-1-1-1-1-11-1-1111-11    linear of order 2
ρ7111111111-1-1-1-1-1111-1-1-11-1-11-11-111    linear of order 2
ρ8111111111-1-1-1-11-1-1-1111-1-1-111-111-1    linear of order 2
ρ911-1-11-11-111-11-1-ii-iii-ii-i1-1-1ii-i1-i    linear of order 4
ρ1011-1-11-11-11-1111ii-ii-ii-i-i-1-11i-i-i-1i    linear of order 4
ρ1111-1-11-11-111-1-1-1-ii-iii-ii-i111-i-ii-1i    linear of order 4
ρ1211-1-11-11-11-11-11ii-ii-ii-i-i-11-1-iii1-i    linear of order 4
ρ1311-1-11-11-111-11-1i-ii-i-ii-ii1-1-1-i-ii1i    linear of order 4
ρ1411-1-11-11-11-1111-i-ii-ii-iii-1-11-iii-1-i    linear of order 4
ρ1511-1-11-11-111-1-1-1i-ii-i-ii-ii111ii-i-1-i    linear of order 4
ρ1611-1-11-11-11-11-11-i-ii-ii-iii-11-1i-i-i1i    linear of order 4
ρ1722-2222-2-2-22-20200000000-20000000    orthogonal lifted from D4
ρ1822-2222-2-2-2-220-20000000020000000    orthogonal lifted from D4
ρ1922-22-2-222-2000002-2-2000200000000    orthogonal lifted from D4
ρ20222-22-2-22-2220-200000000-20000000    orthogonal lifted from D4
ρ21222-22-2-22-2-2-2020000000020000000    orthogonal lifted from D4
ρ2222-22-2-222-200000-222000-200000000    orthogonal lifted from D4
ρ2322-2-2-22-2220000-200022-2000000000    orthogonal lifted from D4
ρ2422-2-2-22-22200002000-2-22000000000    orthogonal lifted from D4
ρ25222-2-222-2-200000-2i-2i2i0002i00000000    complex lifted from C4○D4
ρ26222-2-222-2-2000002i2i-2i000-2i00000000    complex lifted from C4○D4
ρ272222-2-2-2-220000-2i000-2i2i2i000000000    complex lifted from C4○D4
ρ282222-2-2-2-2200002i0002i-2i-2i000000000    complex lifted from C4○D4
ρ298-8000000000000000000000000000    orthogonal faithful

Permutation representations of C24.28D4
On 16 points - transitive group 16T218
Generators in S16
(2 11)(3 13)(4 6)(5 12)(8 16)(9 14)
(2 16)(4 14)(6 9)(8 11)
(1 7)(2 11)(3 5)(4 9)(6 14)(8 16)(10 15)(12 13)
(1 15)(2 16)(3 13)(4 14)(5 12)(6 9)(7 10)(8 11)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)
(1 14 15 4)(2 13 16 3)(5 11 12 8)(6 10 9 7)

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

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

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

G:=TransitiveGroup(16,218);

On 16 points - transitive group 16T224
Generators in S16
(1 5)(2 6)(3 10)(4 11)(7 13)(8 14)(9 16)(12 15)
(1 5)(2 9)(3 7)(4 11)(6 16)(8 14)(10 13)(12 15)
(1 15)(3 13)(5 12)(7 10)
(1 15)(2 16)(3 13)(4 14)(5 12)(6 9)(7 10)(8 11)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)
(1 3 15 13)(2 9 16 6)(4 8 14 11)(5 10 12 7)

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

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

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

G:=TransitiveGroup(16,224);

On 16 points - transitive group 16T268
Generators in S16
(1 10)(2 8)(3 5)(4 9)(6 14)(7 15)(11 16)(12 13)
(1 3)(2 14)(4 16)(5 10)(6 8)(7 12)(9 11)(13 15)
(2 16)(4 14)(6 9)(8 11)
(1 15)(2 16)(3 13)(4 14)(5 12)(6 9)(7 10)(8 11)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)
(1 3 15 13)(2 14 16 4)(5 10 12 7)(6 11 9 8)

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

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

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

G:=TransitiveGroup(16,268);

On 16 points - transitive group 16T284
Generators in S16
(2 16)(3 13)(5 12)(6 9)
(2 16)(4 14)(6 9)(8 11)
(2 16)(4 14)(5 12)(7 10)
(1 15)(2 16)(3 13)(4 14)(5 12)(6 9)(7 10)(8 11)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)
(1 6 15 9)(2 5 16 12)(3 11 13 8)(4 10 14 7)

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

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

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

G:=TransitiveGroup(16,284);

On 16 points - transitive group 16T295
Generators in S16
(1 9)(2 10)(3 15)(4 14)(5 13)(6 16)(7 12)(8 11)
(1 8)(3 5)(9 11)(13 15)
(1 8)(4 6)(9 11)(14 16)
(1 8)(2 7)(3 5)(4 6)(9 11)(10 12)(13 15)(14 16)
(1 2)(3 4)(5 6)(7 8)(9 10 11 12)(13 14 15 16)
(1 16 8 14)(2 13 7 15)(3 12 5 10)(4 9 6 11)

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

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

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

G:=TransitiveGroup(16,295);

On 16 points - transitive group 16T304
Generators in S16
(1 11)(2 12)(3 10)(4 9)(5 13)(6 14)(7 16)(8 15)
(1 5)(2 7)(3 6)(4 8)(9 15)(10 14)(11 13)(12 16)
(1 4)(5 8)(9 11)(13 15)
(1 4)(2 3)(5 8)(6 7)(9 11)(10 12)(13 15)(14 16)
(1 2)(3 4)(5 6)(7 8)(9 10 11 12)(13 14 15 16)
(1 13 4 15)(2 12 3 10)(5 9 8 11)(6 16 7 14)

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

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

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

G:=TransitiveGroup(16,304);

On 16 points - transitive group 16T318
Generators in S16
(1 2)(3 9)(4 12)(5 8)(6 15)(7 14)(10 11)(13 16)
(1 3)(2 9)(4 11)(5 7)(6 16)(8 14)(10 12)(13 15)
(1 3)(2 9)(4 11)(5 15)(6 8)(7 13)(10 12)(14 16)
(1 10)(2 11)(3 12)(4 9)(5 13)(6 14)(7 15)(8 16)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)
(1 13 10 5)(2 6 11 14)(3 7 12 15)(4 16 9 8)

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

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

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

G:=TransitiveGroup(16,318);

On 16 points - transitive group 16T326
Generators in S16
(1 9)(2 16)(3 13)(4 12)(5 10)(6 15)(7 11)(8 14)
(2 8)(4 5)(10 12)(14 16)
(1 3)(2 5)(4 8)(6 7)(9 13)(10 16)(11 15)(12 14)
(1 7)(2 8)(3 6)(4 5)(9 11)(10 12)(13 15)(14 16)
(1 2)(3 4)(5 6)(7 8)(9 10 11 12)(13 14 15 16)
(1 12 7 10)(2 11 8 9)(3 14 6 16)(4 13 5 15)

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

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

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

G:=TransitiveGroup(16,326);

Matrix representation of C24.28D4 in GL8(ℤ)

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

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

C24.28D4 in GAP, Magma, Sage, TeX

C_2^4._{28}D_4
% in TeX

G:=Group("C2^4.28D4");
// GroupNames label

G:=SmallGroup(128,645);
// by ID

G=gap.SmallGroup(128,645);
# by ID

G:=PCGroup([7,-2,2,2,-2,2,2,-2,224,141,288,422,2019,1018,521,2804,1411,2028,1027]);
// Polycyclic

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

Export

Character table of C24.28D4 in TeX

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