Finite Group Databasebeta

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C4×C5×#13108656 #45656332

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

Aliases

direct productC4×C5×#13108656

Splittings

derived, SylowC181 ⋊ C4×C5×C9
HallC4×C5×C181 ⋊ C9
HallC5×C181 ⋊ C4×C9
HallC4×C181 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5C181⋊C3
commutator, hypocenterC181C4×C5×C9
FrattiniC2×C3C2×C5×C181⋊C3
FittingC3×C4×C5×C181C3
socle, prime radicalC2×C3×C5×C181C2×C3
cosocleC2×C3×C181C2×C3×C5
LCSG ▷ C181
UCSC1 ◁ C3×C4×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 3);