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C2×D3729 #28417588

order14916
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD7458
direct productC2×D3729
unambiguous semidirect product(C2×C3)⋊D1243
unambiguous semidirect product(C2×C11)⋊D339
unambiguous semidirect product(C2×C113)⋊D33

Splittings

Fitting, socleC2×C3×C11×C113 ⋊ C2
derived, HallC3×C11×C113 ⋊ C22
HallC11×C113 ⋊ C2×D3
HallC3×C113 ⋊ C2×D11
SylowC113 ⋊ C2×D33
HallC3×C11 ⋊ C2×D113
SylowC11 ⋊ C2×D339
SylowC3 ⋊ C2×D1243

Subgroups

subgroupG/H
center, hypercenterC2D3729
commutator, cosocle, hypocenterC3×C11×C113C22
FrattiniC1G
Fitting, socleC2×C3×C11×C113C2
LCSG ▷ C3×C11×C113
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 129
transitive degreeμt(G) = 7458

A minimal faithful permutation representation — 2 generators on 129 points:

(1,2)(3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129);(4,5)(7,16)(8,15)(9,14)(10,13)(11,12)(18,129)(19,128)(20,127)(21,126)(22,125)(23,124)(24,123)(25,122)(26,121)(27,120)(28,119)(29,118)(30,117)(31,116)(32,115)(33,114)(34,113)(35,112)(36,111)(37,110)(38,109)(39,108)(40,107)(41,106)(42,105)(43,104)(44,103)(45,102)(46,101)(47,100)(48,99)(49,98)(50,97)(51,96)(52,95)(53,94)(54,93)(55,92)(56,91)(57,90)(58,89)(59,88)(60,87)(61,86)(62,85)(63,84)(64,83)(65,82)(66,81)(67,80)(68,79)(69,78)(70,77)(71,76)(72,75)(73,74)

Conjugacy classes & character table

3732 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD14916
maximal normal subgroup ofD14916
maximal quotient ofD14916, Dic7458

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14916, 22);