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C4×C43⋊C9 #13095409

order1548
isoclinismisoclinic class of C43⋊C3
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C43⋊C9
unambiguous semidirect product(C4×C43)⋊C9

Splittings

derived, SylowC43 ⋊ C4×C9
HallC4×C43 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC3×C4C43⋊C3
commutator, hypocenterC43C4×C9
FrattiniC2×C3C2×C43⋊C3
FittingC3×C4×C43C3
socle, prime radical, cosocleC2×C3×C43C2×C3
LCSG ▷ C43
UCSC1 ◁ C3×C4

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 1548

A minimal faithful permutation representation — 2 generators on 56 points:

(1,2,3,4)(6,7,9)(8,11,16)(10,14,13)(12,18,26)(15,21,23)(17,24,20)(19,28,37)(22,30,35)(25,33,32)(27,36,29)(31,40,44)(34,41,43)(38,45,39)(42,46,47)(48,49,51,50,52,54,53,55,56);(5,6,8,12,19,24,9,13,20,29,39,36,16,23,32,28,38,45,26,35,43,40,18,27,37,44,47,46,30,11,17,25,34,42,41,21,7,10,15,22,31,33,14)

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×(C43⋊C7)⋊C9, Dic7×C43⋊C9, #24925424, …
maximal normal subgroup ofC4×(C43⋊C7)⋊C9, C4×C7×C43⋊C9, C4×C11×C43⋊C9, …
maximal quotient ofDic7×C43⋊C9, #24925424, #24925425, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1548, 2);