Finite Group Databasebeta

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C9×#10624382⋊C5 #45656351

order32580
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×#10624382⋊C5
unambiguous semidirect product(C9×#10624382)⋊C5

Splittings

Fitting, HallC9×C181 ⋊ C4×C5
derived, SylowC181 ⋊ C4×C5×C9
HallC9×C181⋊C5 ⋊ C4
HallC9×#10624382 ⋊ C5
HallC181⋊C5 ⋊ C4×C9
Hall#10624382 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC9#10624382⋊C5
commutator, hypocenterC181C4×C5×C9
FrattiniC3C3×#10624382⋊C5
FittingC9×C181C4×C5
socleC3×C181C3×C4×C5
prime radicalC3×D181⋊C5C2×C3
cosocleC3×D181C2×C3×C5
LCSG ▷ C181
UCSC1 ◁ C9

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

261 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 22);