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C9×AGL(1,𝔽23) #17986900

order4554
isoclinismisoclinic class of AGL(1,𝔽23)
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C9×C11)
unambiguous semidirect product(C23⋊C11)⋊(C2×C9)
unambiguous semidirect product(C9×D23)⋊C11

Splittings

Fitting, HallC9×C23 ⋊ C2×C11
derived, SylowC23 ⋊ C2×C9×C11
HallC9×C23⋊C11 ⋊ C2
HallC9×D23 ⋊ C11
HallC23⋊C11 ⋊ C2×C9
HallD23 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC9AGL(1,𝔽23)
commutator, hypocenterC23C2×C9×C11
FrattiniC3C3×AGL(1,𝔽23)
FittingC9×C23C2×C11
socle, cosocleC3×C23C2×C3×C11
prime radicalC3×AGL(1,𝔽23)C3
LCSG ▷ C23
UCSC1 ◁ C9

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)(11,14,15,22,23,30,25,26,16,27,28,12,13,17,18,29,24,19,31,20,21,32);(10,11,13,16,15,19,21,29,18,24,26,32,28,31,30,22,23,27,25,17,20,14,12)

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C9×AGL(1,𝔽23), C9×C5⋊AGL(1,𝔽23), C7×C9×AGL(1,𝔽23), …
maximal normal subgroup ofC5×C9×AGL(1,𝔽23), C7×C9×AGL(1,𝔽23), 3−1+2×AGL(1,𝔽23)
maximal quotient ofC5×C9×AGL(1,𝔽23), C9×C5⋊AGL(1,𝔽23), C7×C9×AGL(1,𝔽23), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 2);