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C5×Dic1629 #45656338

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

Aliases

direct productC5×Dic1629
unambiguous semidirect productC9⋊(C5×Dic181)

Splittings

derived, HallC9×C181 ⋊ C4×C5
HallC5×C9×C181 ⋊ C4
HallC5×C181 ⋊ Dic9
SylowC181 ⋊ C5×Dic9
HallC5×C9 ⋊ Dic181
SylowC9 ⋊ C5×Dic181

Subgroups

subgroupG/H
center, hypercenterC2×C5D1629
commutator, hypocenterC9×C181C4×C5
FrattiniC2×C3C5×D543
FittingC2×C5×C9×C181C2
socle, prime radicalC2×C3×C5×C181D3
cosocleC2×C9×C181C2×C5
LCSG ▷ C9×C181
UCSC1 ◁ C2×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 9);