Finite Group Databasebeta

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C4×#13108656⋊C5 #45656333

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

Aliases

direct productC4×#13108656⋊C5
unambiguous semidirect product(C4×#13108656)⋊C5

Splittings

derived, SylowC181 ⋊ C4×C5×C9
HallC4×#13108656 ⋊ C5
HallC4×C181⋊C5 ⋊ C9
Hall#13108656 ⋊ C4×C5
HallC181⋊C5 ⋊ C4×C9
HallC4×C181 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4(C181⋊C3)⋊C5
commutator, hypocenterC181C4×C5×C9
FrattiniC2×C3C2×(C181⋊C3)⋊C5
FittingC3×C4×C181C3×C5
socle, cosocleC2×C3×C181C2×C3×C5
prime radicalC2×C3×C181⋊C5C2×C3
LCSG ▷ C181
UCSC1 ◁ C3×C4

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

324 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 4);