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C2×D9381 #49176191

order37524
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD18762
direct productC2×D9381
unambiguous semidirect product(C2×C3)⋊D3127
unambiguous semidirect product(C2×C53)⋊D177
unambiguous semidirect product(C2×C59)⋊D159

Splittings

Fitting, socleC2×C3×C53×C59 ⋊ C2
derived, HallC3×C53×C59 ⋊ C22
HallC53×C59 ⋊ C2×D3
HallC3×C59 ⋊ C2×D53
HallC3×C53 ⋊ C2×D59
SylowC59 ⋊ C2×D159
SylowC53 ⋊ C2×D177
SylowC3 ⋊ C2×D3127

Subgroups

subgroupG/H
center, hypercenterC2D9381
commutator, cosocle, hypocenterC3×C53×C59C22
FrattiniC1G
Fitting, socleC2×C3×C53×C59C2
LCSG ▷ C3×C53×C59
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 117
transitive degreeμt(G) = 18762

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

Conjugacy classes & character table

9384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37524, 28);