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C2×C9×C181⋊C5 #30654307

order16290
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C9×C181⋊C5
unambiguous semidirect product(C2×C9×C181)⋊C5

Splittings

Fitting, HallC2×C9×C181 ⋊ C5
derived, SylowC181 ⋊ C2×C5×C9
HallC9×C181 ⋊ C2×C5
HallC2×C181 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9C181⋊C5
commutator, hypocenterC181C2×C5×C9
FrattiniC3C2×C3×C181⋊C5
FittingC2×C9×C181C5
socleC2×C3×C181C3×C5
prime radicalC2×C3×C181⋊C5C3
cosocleC3×C181C2×C3×C5
LCSG ▷ C181
UCSC1 ◁ C2×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

738 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C9×C181⋊C5, C9×Dic181⋊C5, Dic9×C181⋊C5, …
maximal normal subgroup ofC4×C9×C181⋊C5, C9×Dic181⋊C5, Dic9×C181⋊C5, …
maximal quotient ofC4×C9×C181⋊C5, C22×C9×C181⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16290, 2);