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C2×C5×D9×C181 #45656396

order32580
isoclinismisoclinic class of D9
automorphism?
homologyAbelianization (H1) = C22×C5×C181 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D9×C181
unambiguous semidirect productC9⋊(C22×C5×C181)
unambiguous semidirect product(C2×C9)⋊(C2×C5×C181)

Splittings

FittingC2×C5×C9×C181 ⋊ C2
derived, SylowC9 ⋊ C22×C5×C181
HallC5×C9×C181 ⋊ C22
HallC9×C181 ⋊ C22×C5
HallC5×C9 ⋊ C22×C181

Subgroups

subgroupG/H
center, hypercenterC2×C5×C181D9
commutator, cosocle, hypocenterC9C22×C5×C181
FrattiniC3C2×C5×D3×C181
FittingC2×C5×C9×C181C2
socleC2×C3×C5×C181D3
LCSG ▷ C9
UCSC1 ◁ C2×C5×C181

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 67);