Finite Group Databasebeta

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C5×Dic9×C181 #45656337

order32580
isoclinismisoclinic class of D9
automorphism?
homologyAbelianization (H1) = C4×C5×C181 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic9×C181
unambiguous semidirect productC9⋊(C4×C5×C181)

Splittings

derived, SylowC9 ⋊ C4×C5×C181
HallC5×C9×C181 ⋊ C4
HallC9×C181 ⋊ C4×C5
HallC5×C9 ⋊ C4×C181

Subgroups

subgroupG/H
center, hypercenterC2×C5×C181D9
commutator, hypocenterC9C4×C5×C181
FrattiniC2×C3C5×D3×C181
FittingC2×C5×C9×C181C2
socle, prime radicalC2×C3×C5×C181D3
cosocleC2×C9C2×C5×C181
LCSG ▷ C9
UCSC1 ◁ C2×C5×C181

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 8);