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C13⋊C3×C23⋊C11 #23754530

order9867
automorphism?
homologyAbelianization (H1) = C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×C23⋊C11
unambiguous semidirect productC13⋊(C3×C23⋊C11)
unambiguous semidirect productC23⋊(C11×C13⋊C3)
unambiguous semidirect product(C23×C13⋊C3)⋊C11
unambiguous semidirect product(C13×C23⋊C11)⋊C3

Splittings

Fitting, socle, derived, HallC13×C23 ⋊ C3×C11
HallC13×C23⋊C11 ⋊ C3
HallC23×C13⋊C3 ⋊ C11
SylowC23 ⋊ C11×C13⋊C3
SylowC13 ⋊ C3×C23⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C23C3×C11
LCSG ▷ C13×C23
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

91 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C13⋊C3×C23⋊C11, C13⋊C3×AGL(1,𝔽23), D13⋊C3×C23⋊C11, …
maximal normal subgroup ofC2×C13⋊C3×C23⋊C11, C13⋊C3×AGL(1,𝔽23), D13⋊C3×C23⋊C11, …
maximal quotient ofC2×C13⋊C3×C23⋊C11, C13⋊C9×C23⋊C11, C3×C13⋊C3×C23⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9867, 4);