Finite Group Databasebeta

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C2×C9×D61⋊C5 #24926685

order10980
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C9D61⋊C5
commutator, hypocenterC61C22×C5×C9
FrattiniC3C2×C3×D61⋊C5
FittingC2×C9×C61C2×C5
socleC2×C3×C61C2×C3×C5
prime radicalC2×C3×D61⋊C5C3
cosocleC3×C61C22×C3×C5
LCSG ▷ C61
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

288 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 35);