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C4×(C61⋊C5)⋊C9 #24926653

order10980
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×(C61⋊C5)⋊C9
unambiguous semidirect product(C4×C61⋊C5)⋊C9
unambiguous semidirect product(C4×C61⋊C9)⋊C5

Splittings

derived, SylowC61 ⋊ C4×C5×C9
HallC4×C61⋊C9 ⋊ C5
HallC4×C61⋊C5 ⋊ C9
HallC61⋊C9 ⋊ C4×C5
HallC61⋊C5 ⋊ C4×C9
HallC4×C61 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4(C61⋊C3)⋊C5
commutator, hypocenterC61C4×C5×C9
FrattiniC2×C3C2×(C61⋊C3)⋊C5
FittingC3×C4×C61C3×C5
socle, cosocleC2×C3×C61C2×C3×C5
prime radicalC2×C3×C61⋊C5C2×C3
LCSG ▷ C61
UCSC1 ◁ C3×C4

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 3);