Finite Group Databasebeta

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C9×C11×C23⋊C11 #38736747

order25047
automorphism?
homologyAbelianization (H1) = C9×C112 · Schur multiplier (H2) = C11

Aliases

direct productC9×C11×C23⋊C11
unambiguous semidirect productC23⋊(C9×C112)
unambiguous semidirect product(C9×C23)⋊C112
unambiguous semidirect product(C11×C23)⋊(C9×C11)
unambiguous semidirect product(C9×C11×C23)⋊C11

Splittings

FittingC9×C11×C23 ⋊ C11
derived, SylowC23 ⋊ C9×C112
HallC9×C23 ⋊ C112

Subgroups

subgroupG/H
center, hypercenterC9×C11C23⋊C11
commutator, hypocenterC23C9×C112
FrattiniC3C3×C11×C23⋊C11
FittingC9×C11×C23C11
socleC3×C11×C23C3×C11
prime radicalC3×C11×C23⋊C11C3
cosocleC3×C23C3×C112
LCSG ▷ C23
UCSC1 ◁ C9×C11

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2277

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25047, 6);