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C9⋊AGL(1,𝔽23) #17986902

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

Aliases

unambiguous semidirect productC9⋊AGL(1,𝔽23)
unambiguous semidirect product(C23⋊C11)⋊D9
unambiguous semidirect productD207⋊C11

Splittings

Fitting, derived, HallC9×C23 ⋊ C2×C11
HallC9×C23⋊C11 ⋊ C2
HallD207 ⋊ C11
HallC23⋊C11 ⋊ D9
SylowC23 ⋊ C11×D9
SylowC9 ⋊ AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C23C2×C11
FrattiniC3C3⋊AGL(1,𝔽23)
socleC3×C23D3×C11
LCSG ▷ C9×C23
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2,11,3,23,3|c^3=e^2,c^a=c^2e,d^a=d^22,e^a=e^2,d^b=d^3

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C9⋊AGL(1,𝔽23), C5⋊(C9⋊AGL(1,𝔽23)), C7×C9⋊AGL(1,𝔽23), …
maximal normal subgroup ofC5×C9⋊AGL(1,𝔽23), C7×C9⋊AGL(1,𝔽23), #72275867
maximal quotient ofC5×C9⋊AGL(1,𝔽23), C5⋊(C9⋊AGL(1,𝔽23)), C7×C9⋊AGL(1,𝔽23), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 4);