Finite Group Databasebeta

← Prev (#45656397) Next (#45656399) →

C2×C9×D5×C181 #45656398

order32580
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C9×C181 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D5×C181
unambiguous semidirect productC5⋊(C22×C9×C181)
unambiguous semidirect product(C2×C5)⋊(C2×C9×C181)

Splittings

FittingC2×C5×C9×C181 ⋊ C2
derived, SylowC5 ⋊ C22×C9×C181
HallC5×C9×C181 ⋊ C22
HallC5×C181 ⋊ C22×C9
HallC5×C9 ⋊ C22×C181

Subgroups

subgroupG/H
center, hypercenterC2×C9×C181D5
commutator, hypocenterC5C22×C9×C181
FrattiniC3C2×C3×D5×C181
FittingC2×C5×C9×C181C2
socleC2×C3×C5×C181C2×C3
prime radicalC2×C3×D5×C181C3
cosocleC3×C5C22×C3×C181
LCSG ▷ C5
UCSC1 ◁ C2×C9×C181

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 69);