Finite Group Databasebeta

← Prev (#45656389) Next (#45656391) →

C5×C22⋊#13108656 #45656390

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

Aliases

direct productC5×C22⋊#13108656
unambiguous semidirect productC22⋊(C5×#13108656)
unambiguous semidirect product(C22×C5)⋊#13108656

Splittings

derived, HallC22×C181 ⋊ C5×C9
HallC22×C5×C181 ⋊ C9
HallC5×C181 ⋊ C22⋊C9
SylowC181 ⋊ C5×C22⋊C9
HallC22×C5 ⋊ #13108656
SylowC22 ⋊ C5×#13108656

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊(C181⋊C3)
commutator, hypocenterC22×C181C5×C9
FrattiniC3C5×C22⋊(C181⋊C3)
Fitting, socle, prime radicalC22×C3×C5×C181C3
cosocleC22×C3×C181C3×C5
LCSG ▷ C22×C181
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3660 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 61);