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C2×D9×C181⋊C5 #45656366

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

Aliases

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

Splittings

FittingC2×C9×C181 ⋊ C2×C5
derived, HallC9×C181 ⋊ C22×C5
HallC9×C181⋊C5 ⋊ C22
HallC2×D9×C181 ⋊ C5
SylowC181 ⋊ C2×C5×D9
SylowC9 ⋊ C22×C181⋊C5

Subgroups

subgroupG/H
center, hypercenterC2D9×C181⋊C5
commutator, cosocle, hypocenterC9×C181C22×C5
FrattiniC3C2×D3×C181⋊C5
FittingC2×C9×C181C2×C5
socleC2×C3×C181C5×D3
LCSG ▷ C9×C181
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

492 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 37);