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C2×(D61⋊C5)⋊C9 #24926671

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

Aliases

direct productC2×(D61⋊C5)⋊C9
unambiguous semidirect product(D61⋊C5)⋊(C2×C9)
unambiguous semidirect product(D61⋊C9)⋊(C2×C5)
unambiguous semidirect product(C2×D61⋊C5)⋊C9
unambiguous semidirect product(C2×D61⋊C9)⋊C5
unambiguous semidirect product((C61⋊C5)⋊C9)⋊C22
unambiguous semidirect product(C2×(C61⋊C5)⋊C9)⋊C2

Splittings

derived, SylowC61 ⋊ C22×C5×C9
Hall(C61⋊C5)⋊C9 ⋊ C22
HallC2×D61⋊C9 ⋊ C5
HallC2×D61⋊C5 ⋊ C9
HallC61⋊C9 ⋊ C22×C5
HallC61⋊C5 ⋊ C22×C9
HallC2×D61 ⋊ C5×C9

Subgroups

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

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 21);