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C2×D9095 #49138558

order36380
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD18190
direct productC2×D9095
unambiguous semidirect product(C2×C5)⋊D1819
unambiguous semidirect product(C2×C17)⋊D535
unambiguous semidirect product(C2×C107)⋊D85

Splittings

Fitting, socleC2×C5×C17×C107 ⋊ C2
derived, HallC5×C17×C107 ⋊ C22
HallC17×C107 ⋊ C2×D5
HallC5×C107 ⋊ C2×D17
SylowC107 ⋊ C2×D85
HallC5×C17 ⋊ C2×D107
SylowC17 ⋊ C2×D535
SylowC5 ⋊ C2×D1819

Subgroups

subgroupG/H
center, hypercenterC2D9095
commutator, cosocle, hypocenterC5×C17×C107C22
FrattiniC1G
Fitting, socleC2×C5×C17×C107C2
LCSG ▷ C5×C17×C107
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 131
transitive degreeμt(G) = 18190

A minimal faithful permutation representation — 2 generators on 131 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);(4,7)(5,6)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(26,131)(27,130)(28,129)(29,128)(30,127)(31,126)(32,125)(33,124)(34,123)(35,122)(36,121)(37,120)(38,119)(39,118)(40,117)(41,116)(42,115)(43,114)(44,113)(45,112)(46,111)(47,110)(48,109)(49,108)(50,107)(51,106)(52,105)(53,104)(54,103)(55,102)(56,101)(57,100)(58,99)(59,98)(60,97)(61,96)(62,95)(63,94)(64,93)(65,92)(66,91)(67,90)(68,89)(69,88)(70,87)(71,86)(72,85)(73,84)(74,83)(75,82)(76,81)(77,80)(78,79)

Conjugacy classes & character table

9098 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36380, 35);