Finite Group Databasebeta

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Dic45×C181 #45656339

order32580
isoclinismisoclinic class of D45
automorphism?
homologyAbelianization (H1) = C4×C181 · Schur multiplier (H2) = C1

Aliases

direct productDic45×C181
unambiguous semidirect productC9⋊(Dic5×C181)

Splittings

derived, HallC5×C9 ⋊ C4×C181
HallC5×C9×C181 ⋊ C4
HallC9×C181 ⋊ Dic5
HallC5×C181 ⋊ Dic9
SylowC9 ⋊ Dic5×C181
SylowC5 ⋊ Dic9×C181

Subgroups

subgroupG/H
center, hypercenterC2×C181D45
commutator, hypocenterC5×C9C4×C181
FrattiniC2×C3D15×C181
FittingC2×C5×C9×C181C2
socle, prime radicalC2×C3×C5×C181D3
cosocleC2×C5×C9C2×C181
LCSG ▷ C5×C9
UCSC1 ◁ C2×C181

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 10);