Finite Group Databasebeta

← Prev (#45656401) Next (#45656403) →

C4×#13108658⋊C5 #45656402

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

Aliases

direct productC4×#13108658⋊C5
unambiguous semidirect product(C4×#13108658)⋊C5

Splittings

Fitting, HallC4×C181 ⋊ C5×C9
derived, SylowC181 ⋊ C4×C5×C9
HallC4×#13108658 ⋊ C5
HallC4×C181⋊C5 ⋊ C9
Hall#13108658 ⋊ C4×C5
HallC181⋊C5 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC4#13108658⋊C5
commutator, hypocenterC181C4×C5×C9
FrattiniC2C2×#13108658⋊C5
FittingC4×C181C5×C9
socleC2×C181C2×C5×C9
prime radicalC2×(C181⋊C3)⋊C5C2×C3
cosocleC2×C181⋊C3C2×C3×C5
LCSG ▷ C181
UCSC1 ◁ C4

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 73);