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C2×D8085 #44568436

order32340
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16170
direct productC2×D8085
unambiguous semidirect product(C2×C3)⋊D2695
unambiguous semidirect product(C2×C5)⋊D1617
unambiguous semidirect product(C2×C11)⋊D735
unambiguous semidirect product(C2×C49)⋊D165

Splittings

FittingC2×C3×C5×C11×C49 ⋊ C2
derived, HallC3×C5×C11×C49 ⋊ C22
HallC5×C11×C49 ⋊ C2×D3
HallC3×C11×C49 ⋊ C2×D5
HallC3×C5×C49 ⋊ C2×D11
HallC11×C49 ⋊ C2×D15
HallC5×C49 ⋊ C2×D33
HallC3×C5×C11 ⋊ C2×D49
HallC3×C49 ⋊ C2×D55
HallC5×C11 ⋊ C2×D147
SylowC49 ⋊ C2×D165
HallC3×C11 ⋊ C2×D245
HallC3×C5 ⋊ C2×D539
SylowC11 ⋊ C2×D735
SylowC5 ⋊ C2×D1617
SylowC3 ⋊ C2×D2695

Subgroups

subgroupG/H
center, hypercenterC2D8085
commutator, cosocle, hypocenterC3×C5×C11×C49C22
FrattiniC7C2×D1155
FittingC2×C3×C5×C11×C49C2
socleC2×C3×C5×C7×C11D7
LCSG ▷ C3×C5×C11×C49
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 70
transitive degreeμt(G) = 16170

A minimal faithful permutation representation — 2 generators on 70 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);(4,5)(7,10)(8,9)(12,59)(13,58)(14,57)(15,56)(16,55)(17,54)(18,53)(19,52)(20,51)(21,50)(22,49)(23,48)(24,47)(25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(61,70)(62,69)(63,68)(64,67)(65,66)

Conjugacy classes & character table

8088 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD32340
maximal normal subgroup ofD32340
maximal quotient ofDic16170, D32340

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 138);