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C2×C5⋊(#13108656⋊C2) #45656368

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

Aliases

direct productC2×C5⋊(#13108656⋊C2)
unambiguous semidirect product(C2×C5)⋊(#13108656⋊C2)
unambiguous semidirect product(C2×#13108656)⋊D5

Splittings

derived, HallC5×C181 ⋊ C22×C9
HallC5×#13108656 ⋊ C22
HallC2×D905 ⋊ C9
Hall#13108656 ⋊ C2×D5
SylowC181 ⋊ C2×C9×D5
SylowC5 ⋊ C2×#13108656⋊C2

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D181⋊C3)
commutator, hypocenterC5×C181C22×C9
FrattiniC3C2×C5⋊(D181⋊C3)
Fitting, socleC2×C3×C5×C181C2×C3
prime radicalC2×C3×D905C3
cosocleC3×C5×C181C22×C3
LCSG ▷ C5×C181
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

972 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 39);