Finite Group Databasebeta

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C22×C32×C61⋊C5 #24926805

order10980
isoclinismisoclinic class of C61⋊C5
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C32×C61⋊C5
unambiguous semidirect product(C22×C32×C61)⋊C5

Splittings

Fitting, socle, HallC22×C32×C61 ⋊ C5
derived, SylowC61 ⋊ C22×C32×C5
HallC32×C61 ⋊ C22×C5
HallC22×C61 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC22×C32C61⋊C5
commutator, cosocle, hypocenterC61C22×C32×C5
FrattiniC1G
Fitting, socleC22×C32×C61C5
LCSG ▷ C61
UCSC1 ◁ C22×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

612 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 155);