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C2×D2937 #26044349

order11748
automorphismAut(G) order 10338240
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD5874
direct productC2×D2937
unambiguous semidirect product(C2×C3)⋊D979
unambiguous semidirect product(C2×C11)⋊D267
unambiguous semidirect product(C2×C89)⋊D33

Splittings

Fitting, socleC2×C3×C11×C89 ⋊ C2
derived, HallC3×C11×C89 ⋊ C22
HallC11×C89 ⋊ C2×D3
HallC3×C89 ⋊ C2×D11
SylowC89 ⋊ C2×D33
HallC3×C11 ⋊ C2×D89
SylowC11 ⋊ C2×D267
SylowC3 ⋊ C2×D979

Subgroups

subgroupG/H
center, hypercenterC2D2937
commutator, cosocle, hypocenterC3×C11×C89C22
FrattiniC1G
Fitting, socleC2×C3×C11×C89C2
LCSG ▷ C3×C11×C89
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 105
transitive degreeμt(G) = 5874

A minimal faithful permutation representation — 2 generators on 105 points:

(1,2)(3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(4,5)(7,16)(8,15)(9,14)(10,13)(11,12)(18,105)(19,104)(20,103)(21,102)(22,101)(23,100)(24,99)(25,98)(26,97)(27,96)(28,95)(29,94)(30,93)(31,92)(32,91)(33,90)(34,89)(35,88)(36,87)(37,86)(38,85)(39,84)(40,83)(41,82)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D8811, D3×D2937, C2×C3×D2937, …
maximal normal subgroup ofC2×C3×D2937, D11748
maximal quotient ofC2×D8811, D3×D2937, C2×C3×D2937, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11748, 34);