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C2×D8041 #44565504

order32164
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16082
direct productC2×D8041
unambiguous semidirect product(C2×C11)⋊D731
unambiguous semidirect product(C2×C17)⋊D473
unambiguous semidirect product(C2×C43)⋊D187

Splittings

Fitting, socleC2×C11×C17×C43 ⋊ C2
derived, HallC11×C17×C43 ⋊ C22
HallC17×C43 ⋊ C2×D11
HallC11×C43 ⋊ C2×D17
HallC11×C17 ⋊ C2×D43
SylowC43 ⋊ C2×D187
SylowC17 ⋊ C2×D473
SylowC11 ⋊ C2×D731

Subgroups

subgroupG/H
center, hypercenterC2D8041
commutator, cosocle, hypocenterC11×C17×C43C22
FrattiniC1G
Fitting, socleC2×C11×C17×C43C2
LCSG ▷ C11×C17×C43
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 16082

A minimal faithful permutation representation — 2 generators on 73 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(32,73)(33,72)(34,71)(35,70)(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)

Conjugacy classes & character table

8044 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD32164
maximal normal subgroup ofD32164
maximal quotient ofDic16082, D32164

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32164, 27);