Finite Group Databasebeta

← Prev (#45656368) Next (#45656370) →

C2×D5×#13108656 #45656369

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

Aliases

direct productC2×D5×#13108656
unambiguous semidirect productC5⋊(C22×#13108656)
unambiguous semidirect product(C2×C5)⋊(C2×#13108656)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×C181⋊C3
commutator, hypocenterC5×C181C22×C9
FrattiniC3C2×D5×C181⋊C3
Fitting, socleC2×C3×C5×C181C2×C3
prime radicalC2×C3×D5×C181C3
cosocleC3×C5×C181C22×C3
LCSG ▷ C5×C181
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 40);