Finite Group Databasebeta

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C5×#92150⋊C9 #36344867

order21780
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C11

Aliases

direct productC5×#92150⋊C9
unambiguous semidirect product(C5×#92150)⋊C9

Splittings

derived, SylowC112 ⋊ C4×C5×C9
HallC5×C112⋊C9 ⋊ C4
HallC5×#92150 ⋊ C9
HallC112⋊C9 ⋊ C4×C5
HallC5×C112 ⋊ C4×C9
Hall#92150 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5#92150⋊C3
commutator, hypocenterC112C4×C5×C9
FrattiniC3C5×#92150⋊C3
Fitting, socleC3×C5×C112C3×C4
prime radicalC3×C5×C11⋊D11C2×C3
cosocleC3×C11⋊D11C2×C3×C5
LCSG ▷ C112
UCSC1 ◁ C3×C5

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

330 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 216);