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Dic9×C181⋊C5 #45656342

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

Aliases

direct productDic9×C181⋊C5
unambiguous semidirect productC9⋊(C4×C181⋊C5)
unambiguous semidirect product(Dic9×C181)⋊C5

Splittings

derived, HallC9×C181 ⋊ C4×C5
HallC9×C181⋊C5 ⋊ C4
HallDic9×C181 ⋊ C5
SylowC181 ⋊ C5×Dic9
SylowC9 ⋊ C4×C181⋊C5

Subgroups

subgroupG/H
center, hypercenterC2D9×C181⋊C5
commutator, hypocenterC9×C181C4×C5
FrattiniC2×C3D3×C181⋊C5
Fitting, cosocleC2×C9×C181C2×C5
socleC2×C3×C181C5×D3
prime radicalC2×C3×C181⋊C5D3
LCSG ▷ C9×C181
UCSC1 ◁ C2

36 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, 13);