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D9×C23⋊C11 #17986901

order4554
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productD9×C23⋊C11
unambiguous semidirect productC9⋊(C2×C23⋊C11)
unambiguous semidirect product(D9×C23)⋊C11

Splittings

Fitting, derived, HallC9×C23 ⋊ C2×C11
HallC9×C23⋊C11 ⋊ C2
HallD9×C23 ⋊ C11
SylowC23 ⋊ C11×D9
SylowC9 ⋊ C2×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C23C2×C11
FrattiniC3D3×C23⋊C11
socleC3×C23D3×C11
LCSG ▷ C9×C23
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 207

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5,6,7,8,9)(11,12,13,15,18,19,24,27,14,17,21)(16,20,25,23,26,31,30,29,32,22,28);(2,9)(3,8)(4,7)(5,6)(10,11,12,14,13,16,17,22,15,19,20,26,21,27,28,32,18,23,24,29,25,30,31)

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D9×C23⋊C11, D45×C23⋊C11, C7×D9×C23⋊C11, …
maximal normal subgroup ofC5×D9×C23⋊C11, C7×D9×C23⋊C11, AGL(1,ℤ/9)×C23⋊C11
maximal quotient ofC5×D9×C23⋊C11, D45×C23⋊C11, C7×D9×C23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 3);