Finite Group Databasebeta

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C9×#92150⋊C5 #36344833

order21780
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×#92150⋊C5
unambiguous semidirect product(C9×#92150)⋊C5

Splittings

Fitting, HallC9×C112 ⋊ C4×C5
derived, SylowC112 ⋊ C4×C5×C9
HallC9×#10597243 ⋊ C4
HallC9×#92150 ⋊ C5
Hall#10597243 ⋊ C4×C9
Hall#92150 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC9#92150⋊C5
commutator, hypocenterC112C4×C5×C9
FrattiniC3C3×#92150⋊C5
FittingC9×C112C4×C5
socleC3×C112C3×C4×C5
prime radicalC3×#11925892C2×C3
cosocleC3×C11⋊D11C2×C3×C5
LCSG ▷ C112
UCSC1 ◁ C9

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 182);