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C2×C9⋊(D61⋊C5) #24926686

order10980
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9⋊(D61⋊C5)
unambiguous semidirect product(C2×C9)⋊(D61⋊C5)
unambiguous semidirect product(C2×C61⋊C5)⋊D9
unambiguous semidirect product(C2×D549)⋊C5

Splittings

FittingC2×C9×C61 ⋊ C2×C5
derived, HallC9×C61 ⋊ C22×C5
HallC9×C61⋊C5 ⋊ C22
HallC2×D549 ⋊ C5
HallC61⋊C5 ⋊ C2×D9
SylowC61 ⋊ C2×C5×D9
SylowC9 ⋊ C2×D61⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C9⋊(D61⋊C5)
commutator, cosocle, hypocenterC9×C61C22×C5
FrattiniC3C2×C3⋊(D61⋊C5)
FittingC2×C9×C61C2×C5
socleC2×C3×C61C5×D3
LCSG ▷ C9×C61
UCSC1 ◁ C2

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(10980, 36);