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C2×(#13108656⋊C2)⋊C5 #45656350

order32580
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×(#13108656⋊C2)⋊C5
unambiguous semidirect product(#13108656⋊C2)⋊(C2×C5)
unambiguous semidirect product(C2×#13108656⋊C2)⋊C5
unambiguous semidirect product(#13108656⋊C5)⋊C22
unambiguous semidirect product(C2×#13108656⋊C5)⋊C2

Splittings

derived, SylowC181 ⋊ C22×C5×C9
Hall#13108656⋊C5 ⋊ C22
HallC2×#13108656⋊C2 ⋊ C5
HallC2×D181⋊C5 ⋊ C9
Hall#13108656 ⋊ C22×C5
HallC181⋊C5 ⋊ C22×C9
HallC2×D181 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3(D181⋊C3)⋊C5
commutator, hypocenterC181C22×C5×C9
FrattiniC3C2×(D181⋊C3)⋊C5
Fitting, socleC2×C3×C181C2×C3×C5
prime radicalC2×C3×D181⋊C5C3
cosocleC3×C181C22×C3×C5
LCSG ▷ C181
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 21);