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C2×D2967 #26045150

order11868
automorphismAut(G) order 10966032
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD5934
direct productC2×D2967
unambiguous semidirect product(C2×C3)⋊D989
unambiguous semidirect product(C2×C23)⋊D129
unambiguous semidirect product(C2×C43)⋊D69

Splittings

Fitting, socleC2×C3×C23×C43 ⋊ C2
derived, HallC3×C23×C43 ⋊ C22
HallC23×C43 ⋊ C2×D3
HallC3×C43 ⋊ C2×D23
HallC3×C23 ⋊ C2×D43
SylowC43 ⋊ C2×D69
SylowC23 ⋊ C2×D129
SylowC3 ⋊ C2×D989

Subgroups

subgroupG/H
center, hypercenterC2D2967
commutator, cosocle, hypocenterC3×C23×C43C22
FrattiniC1G
Fitting, socleC2×C3×C23×C43C2
LCSG ▷ C3×C23×C43
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 71
transitive degreeμt(G) = 5934

A minimal faithful permutation representation — 2 generators on 71 points:

(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)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71);(4,5)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(30,71)(31,70)(32,69)(33,68)(34,67)(35,66)(36,65)(37,64)(38,63)(39,62)(40,61)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)

Conjugacy classes & character table

2970 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D8901, C2×C3⋊(C23⋊(D43⋊C3)), D3×D2967, …
maximal normal subgroup ofC2×C3⋊(C23⋊(D43⋊C3)), C2×C3×D2967, D11868
maximal quotient ofC2×D8901, D3×D2967, C2×C3×D2967, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11868, 28);