Finite Group Databasebeta

← Prev (#45656352) Next (#45656354) →

D9×D181⋊C5 #45656353

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

Aliases

direct productD9×D181⋊C5
unambiguous semidirect productD181⋊(C5×D9)
unambiguous semidirect product(D9×D181)⋊C5
unambiguous semidirect product(C9×D181⋊C5)⋊C2
unambiguous semidirect product(D9×C181⋊C5)⋊C2
unambiguous semidirect product(C9⋊(D181⋊C5))⋊C2

Splittings

Fitting, derived, HallC9×C181 ⋊ C22×C5
HallC9×C181⋊C5 ⋊ C22
HallD9×D181 ⋊ C5
HallC181⋊C5 ⋊ C2×D9
SylowC181 ⋊ C2×C5×D9
SylowC9 ⋊ C2×D181⋊C5

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C181C22×C5
FrattiniC3D3×D181⋊C5
socleC3×C181C2×C5×D3
LCSG ▷ C9×C181
UCSC1

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 24);