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C2×D9185 #49145102

order36740
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD18370
direct productC2×D9185
unambiguous semidirect product(C2×C5)⋊D1837
unambiguous semidirect product(C2×C11)⋊D835
unambiguous semidirect product(C2×C167)⋊D55

Splittings

Fitting, socleC2×C5×C11×C167 ⋊ C2
derived, HallC5×C11×C167 ⋊ C22
HallC11×C167 ⋊ C2×D5
HallC5×C167 ⋊ C2×D11
SylowC167 ⋊ C2×D55
HallC5×C11 ⋊ C2×D167
SylowC11 ⋊ C2×D835
SylowC5 ⋊ C2×D1837

Subgroups

subgroupG/H
center, hypercenterC2D9185
commutator, cosocle, hypocenterC5×C11×C167C22
FrattiniC1G
Fitting, socleC2×C5×C11×C167C2
LCSG ▷ C5×C11×C167
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 185
transitive degreeμt(G) = 18370

A minimal faithful permutation representation — 2 generators on 185 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185);(4,7)(5,6)(9,18)(10,17)(11,16)(12,15)(13,14)(20,185)(21,184)(22,183)(23,182)(24,181)(25,180)(26,179)(27,178)(28,177)(29,176)(30,175)(31,174)(32,173)(33,172)(34,171)(35,170)(36,169)(37,168)(38,167)(39,166)(40,165)(41,164)(42,163)(43,162)(44,161)(45,160)(46,159)(47,158)(48,157)(49,156)(50,155)(51,154)(52,153)(53,152)(54,151)(55,150)(56,149)(57,148)(58,147)(59,146)(60,145)(61,144)(62,143)(63,142)(64,141)(65,140)(66,139)(67,138)(68,137)(69,136)(70,135)(71,134)(72,133)(73,132)(74,131)(75,130)(76,129)(77,128)(78,127)(79,126)(80,125)(81,124)(82,123)(83,122)(84,121)(85,120)(86,119)(87,118)(88,117)(89,116)(90,115)(91,114)(92,113)(93,112)(94,111)(95,110)(96,109)(97,108)(98,107)(99,106)(100,105)(101,104)(102,103)

Conjugacy classes & character table

9188 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36740, 36);