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C2×D5×C61⋊C9 #24926690

order10980
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C61⋊C9
unambiguous semidirect productC5⋊(C22×C61⋊C9)
unambiguous semidirect product(C2×C5)⋊(C2×C61⋊C9)
unambiguous semidirect product(C2×D5×C61)⋊C9

Splittings

derived, HallC5×C61 ⋊ C22×C9
HallC5×C61⋊C9 ⋊ C22
HallC2×D5×C61 ⋊ C9
SylowC61 ⋊ C2×C9×D5
SylowC5 ⋊ C22×C61⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×C61⋊C3
commutator, hypocenterC5×C61C22×C9
FrattiniC3C2×D5×C61⋊C3
Fitting, socleC2×C3×C5×C61C2×C3
prime radicalC2×C3×D5×C61C3
cosocleC3×C5×C61C22×C3
LCSG ▷ C5×C61
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

552 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 40);