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C2×C5×#13108656⋊C2 #45656367

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

Aliases

direct productC2×C5×#13108656⋊C2

Splittings

derived, SylowC181 ⋊ C22×C5×C9
HallC5×#13108656 ⋊ C22
HallC2×C5×D181 ⋊ C9
Hall#13108656 ⋊ C22×C5
HallC5×C181 ⋊ C22×C9
HallC2×D181 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D181⋊C3
commutator, hypocenterC181C22×C5×C9
FrattiniC3C2×C5×D181⋊C3
Fitting, socleC2×C3×C5×C181C2×C3
prime radicalC2×C3×C5×D181C3
cosocleC3×C181C22×C3×C5
LCSG ▷ C181
UCSC1 ◁ C2×C3×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 38);