Finite Group Databasebeta

← Prev (#45656340) Next (#45656342) →

C9×Dic181⋊C5 #45656341

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

Aliases

direct productC9×Dic181⋊C5
unambiguous semidirect product(C9×Dic181)⋊C5

Splittings

derived, SylowC181 ⋊ C4×C5×C9
HallC9×C181⋊C5 ⋊ C4
HallC9×Dic181 ⋊ C5
HallC9×C181 ⋊ C4×C5
HallC181⋊C5 ⋊ C4×C9
HallDic181 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9D181⋊C5
commutator, hypocenterC181C4×C5×C9
FrattiniC2×C3C3×D181⋊C5
FittingC2×C9×C181C2×C5
socle, cosocleC2×C3×C181C2×C3×C5
prime radicalC2×C3×C181⋊C5C2×C3
LCSG ▷ C181
UCSC1 ◁ C2×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

504 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 12);