Finite Group Databasebeta

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D9×D61⋊C5 #24926674

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

Aliases

direct productD9×D61⋊C5
unambiguous semidirect productD61⋊(C5×D9)
unambiguous semidirect product(D9×D61)⋊C5
unambiguous semidirect product(C9×D61⋊C5)⋊C2
unambiguous semidirect product(D9×C61⋊C5)⋊C2
unambiguous semidirect product(C9⋊(D61⋊C5))⋊C2

Splittings

Fitting, derived, HallC9×C61 ⋊ C22×C5
HallC9×C61⋊C5 ⋊ C22
HallD9×D61 ⋊ C5
HallC61⋊C5 ⋊ C2×D9
SylowC61 ⋊ C2×C5×D9
SylowC9 ⋊ C2×D61⋊C5

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C61C22×C5
FrattiniC3D3×D61⋊C5
socleC3×C61C2×C5×D3
LCSG ▷ C9×C61
UCSC1

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 24);