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C2×D9021 #49115378

order36084
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD18042
direct productC2×D9021
unambiguous semidirect product(C2×C3)⋊D3007
unambiguous semidirect product(C2×C31)⋊D291
unambiguous semidirect product(C2×C97)⋊D93

Splittings

Fitting, socleC2×C3×C31×C97 ⋊ C2
derived, HallC3×C31×C97 ⋊ C22
HallC31×C97 ⋊ C2×D3
HallC3×C97 ⋊ C2×D31
SylowC97 ⋊ C2×D93
HallC3×C31 ⋊ C2×D97
SylowC31 ⋊ C2×D291
SylowC3 ⋊ C2×D3007

Subgroups

subgroupG/H
center, hypercenterC2D9021
commutator, cosocle, hypocenterC3×C31×C97C22
FrattiniC1G
Fitting, socleC2×C3×C31×C97C2
LCSG ▷ C3×C31×C97
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 133
transitive degreeμt(G) = 18042

A minimal faithful permutation representation — 2 generators on 133 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);(4,5)(7,36)(8,35)(9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(38,133)(39,132)(40,131)(41,130)(42,129)(43,128)(44,127)(45,126)(46,125)(47,124)(48,123)(49,122)(50,121)(51,120)(52,119)(53,118)(54,117)(55,116)(56,115)(57,114)(58,113)(59,112)(60,111)(61,110)(62,109)(63,108)(64,107)(65,106)(66,105)(67,104)(68,103)(69,102)(70,101)(71,100)(72,99)(73,98)(74,97)(75,96)(76,95)(77,94)(78,93)(79,92)(80,91)(81,90)(82,89)(83,88)(84,87)(85,86)

Conjugacy classes & character table

9024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36084, 76);