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C5×C9×#10624382 #45656371

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

Aliases

direct productC5×C9×#10624382

Splittings

Fitting, HallC5×C9×C181 ⋊ C4
derived, SylowC181 ⋊ C4×C5×C9
HallC9×C181 ⋊ C4×C5
HallC5×C181 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9#10624382
commutator, hypocenterC181C4×C5×C9
FrattiniC3C3×C5×#10624382
FittingC5×C9×C181C4
socleC3×C5×C181C3×C4
prime radicalC3×C5×D181C2×C3
cosocleC3×D181C2×C3×C5
LCSG ▷ C181
UCSC1 ◁ C5×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2205 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 42);