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C2×D4653 #32915908

order18612
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9306
direct productC2×D4653
unambiguous semidirect product(C2×C9)⋊D517
unambiguous semidirect product(C2×C11)⋊D423
unambiguous semidirect product(C2×C47)⋊D99

Splittings

FittingC2×C9×C11×C47 ⋊ C2
derived, HallC9×C11×C47 ⋊ C22
HallC11×C47 ⋊ C2×D9
HallC9×C47 ⋊ C2×D11
HallC9×C11 ⋊ C2×D47
SylowC47 ⋊ C2×D99
SylowC11 ⋊ C2×D423
SylowC9 ⋊ C2×D517

Subgroups

subgroupG/H
center, hypercenterC2D4653
commutator, cosocle, hypocenterC9×C11×C47C22
FrattiniC3C2×D1551
FittingC2×C9×C11×C47C2
socleC2×C3×C11×C47D3
LCSG ▷ C9×C11×C47
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 69
transitive degreeμt(G) = 9306

A minimal faithful permutation representation — 2 generators on 69 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);(4,11)(5,10)(6,9)(7,8)(13,22)(14,21)(15,20)(16,19)(17,18)(24,69)(25,68)(26,67)(27,66)(28,65)(29,64)(30,63)(31,62)(32,61)(33,60)(34,59)(35,58)(36,57)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51)(43,50)(44,49)(45,48)(46,47)

Conjugacy classes & character table

4656 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD18612, C2×D13959
maximal normal subgroup ofD18612
maximal quotient ofDic9306, D18612, C2×D13959

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18612, 18);