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C5×#20266783 #45656406

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

Aliases

direct productC5×#20266783

Splittings

derived, SylowC181 ⋊ C4×C5×C9
HallC5×#13108658 ⋊ C4
HallC5×Dic181 ⋊ C9
Hall#13108658 ⋊ C4×C5
HallC5×C181 ⋊ C4×C9
HallDic181 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5#13108658⋊C2
commutator, hypocenterC181C4×C5×C9
FrattiniC2C5×#13108658⋊C2
Fitting, socleC2×C5×C181C2×C9
prime radicalC2×C5×C181⋊C3C2×C3
cosocleC2×C181⋊C3C2×C3×C5
LCSG ▷ C181
UCSC1 ◁ C2×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

280 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 77);