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C2×D9085 #49138163

order36340
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD18170
direct productC2×D9085
unambiguous semidirect product(C2×C5)⋊D1817
unambiguous semidirect product(C2×C23)⋊D395
unambiguous semidirect product(C2×C79)⋊D115

Splittings

Fitting, socleC2×C5×C23×C79 ⋊ C2
derived, HallC5×C23×C79 ⋊ C22
HallC23×C79 ⋊ C2×D5
HallC5×C79 ⋊ C2×D23
HallC5×C23 ⋊ C2×D79
SylowC79 ⋊ C2×D115
SylowC23 ⋊ C2×D395
SylowC5 ⋊ C2×D1817

Subgroups

subgroupG/H
center, hypercenterC2D9085
commutator, cosocle, hypocenterC5×C23×C79C22
FrattiniC1G
Fitting, socleC2×C5×C23×C79C2
LCSG ▷ C5×C23×C79
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 109
transitive degreeμt(G) = 18170

A minimal faithful permutation representation — 2 generators on 109 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);(4,7)(5,6)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(32,109)(33,108)(34,107)(35,106)(36,105)(37,104)(38,103)(39,102)(40,101)(41,100)(42,99)(43,98)(44,97)(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)

Conjugacy classes & character table

9088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36340, 27);