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C3⋊(C11⋊AGL(1,𝔽23)) #30659961

order16698
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C11⋊AGL(1,𝔽23))
unambiguous semidirect productC11⋊(C3⋊AGL(1,𝔽23))
unambiguous semidirect product(C23⋊C11)⋊D33
unambiguous semidirect productD759⋊C11

Splittings

Fitting, socle, derivedC3×C11×C23 ⋊ C2×C11
HallC3×C11×C23⋊C11 ⋊ C2
HallC11×C23⋊C11 ⋊ D3
HallC3×C23 ⋊ C11×D11
SylowC23 ⋊ C11×D33
SylowC3 ⋊ C11⋊AGL(1,𝔽23)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C23C2×C11
LCSG ▷ C3×C11×C23
UCSC1

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 759

Polycyclic presentation:

2,11,3,11,23|c^a=c^2,d^a=d^10,e^a=e^22,e^b=e^2

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD33×AGL(1,𝔽23), D11×C3⋊AGL(1,𝔽23), D3×C11⋊AGL(1,𝔽23), …
maximal normal subgroup ofD33×AGL(1,𝔽23), D11×C3⋊AGL(1,𝔽23), D3×C11⋊AGL(1,𝔽23), …
maximal quotient ofC3⋊(C11⋊(Dic23⋊C11)), C2×C3⋊(C11⋊AGL(1,𝔽23))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16698, 19);