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C2×C5×D1629 #45656395

order32580
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1629
unambiguous semidirect product(C2×C9)⋊(C5×D181)

Splittings

FittingC2×C5×C9×C181 ⋊ C2
derived, HallC9×C181 ⋊ C22×C5
HallC5×C9×C181 ⋊ C22
HallC5×C181 ⋊ C2×D9
SylowC181 ⋊ C2×C5×D9
HallC5×C9 ⋊ C2×D181
SylowC9 ⋊ C2×C5×D181

Subgroups

subgroupG/H
center, hypercenterC2×C5D1629
commutator, cosocle, hypocenterC9×C181C22×C5
FrattiniC3C2×C5×D543
FittingC2×C5×C9×C181C2
socleC2×C3×C5×C181D3
LCSG ▷ C9×C181
UCSC1 ◁ C2×C5

60 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, 66);