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C22×C3×(C61⋊C3)⋊C5 #24926770

order10980
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×(C61⋊C3)⋊C5
unambiguous semidirect product(C22×C3×C61⋊C3)⋊C5

Splittings

Fitting, socleC22×C3×C61 ⋊ C3×C5
derived, SylowC61 ⋊ C22×C32×C5
HallC22×C3×C61⋊C3 ⋊ C5
HallC22×C61⋊C5 ⋊ C32
HallC3×C61⋊C3 ⋊ C22×C5
HallC61⋊C5 ⋊ C22×C32
HallC22×C61 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC22×C3(C61⋊C3)⋊C5
commutator, cosocle, hypocenterC61C22×C32×C5
FrattiniC1G
Fitting, socleC22×C3×C61C3×C5
LCSG ▷ C61
UCSC1 ◁ C22×C3

120 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, 120);