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C22×#13108656⋊C5 #45656354

order32580
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC22×#13108656⋊C5
unambiguous semidirect product(C22×#13108656)⋊C5

Splittings

derived, SylowC181 ⋊ C22×C5×C9
HallC22×#13108656 ⋊ C5
HallC22×C181⋊C5 ⋊ C9
Hall#13108656 ⋊ C22×C5
HallC181⋊C5 ⋊ C22×C9
HallC22×C181 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC22×C3(C181⋊C3)⋊C5
commutator, hypocenterC181C22×C5×C9
FrattiniC3C22×(C181⋊C3)⋊C5
Fitting, socleC22×C3×C181C3×C5
prime radicalC22×C3×C181⋊C5C3
cosocleC3×C181C22×C3×C5
LCSG ▷ C181
UCSC1 ◁ C22×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

324 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 25);