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C2×D4543 #31827863

order18172
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9086
direct productC2×D4543
unambiguous semidirect product(C2×C7)⋊D649
unambiguous semidirect product(C2×C11)⋊D413
unambiguous semidirect product(C2×C59)⋊D77

Splittings

Fitting, socleC2×C7×C11×C59 ⋊ C2
derived, HallC7×C11×C59 ⋊ C22
HallC11×C59 ⋊ C2×D7
HallC7×C59 ⋊ C2×D11
HallC7×C11 ⋊ C2×D59
SylowC59 ⋊ C2×D77
SylowC11 ⋊ C2×D413
SylowC7 ⋊ C2×D649

Subgroups

subgroupG/H
center, hypercenterC2D4543
commutator, cosocle, hypocenterC7×C11×C59C22
FrattiniC1G
Fitting, socleC2×C7×C11×C59C2
LCSG ▷ C7×C11×C59
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 79
transitive degreeμt(G) = 9086

A minimal faithful permutation representation — 2 generators on 79 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);(4,9)(5,8)(6,7)(11,20)(12,19)(13,18)(14,17)(15,16)(22,79)(23,78)(24,77)(25,76)(26,75)(27,74)(28,73)(29,72)(30,71)(31,70)(32,69)(33,68)(34,67)(35,66)(36,65)(37,64)(38,63)(39,62)(40,61)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)

Conjugacy classes & character table

4546 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD18172, C2×D13629
maximal normal subgroup ofD18172
maximal quotient ofDic9086, D18172, C2×D13629

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18172, 17);