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C5×#20266771 #45656357

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

Aliases

direct productC5×#20266771

Splittings

derived, SylowC181 ⋊ C4×C5×C9
HallC5×#13108656 ⋊ C4
HallC5×#10624382 ⋊ C9
Hall#13108656 ⋊ C4×C5
HallC5×C181 ⋊ C4×C9
Hall#10624382 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5#10624382⋊C3
commutator, hypocenterC181C4×C5×C9
FrattiniC3C5×#10624382⋊C3
Fitting, socleC3×C5×C181C3×C4
prime radicalC3×C5×D181C2×C3
cosocleC3×D181C2×C3×C5
LCSG ▷ C181
UCSC1 ◁ C3×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

405 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 28);