Finite Group Databasebeta

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C22×C3×C5×C43⋊C3 #21440950

order7740
isoclinismisoclinic class of C43⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×C5×C43⋊C3

Splittings

Fitting, socleC22×C3×C5×C43 ⋊ C3
derived, SylowC43 ⋊ C22×C32×C5
HallC22×C5×C43 ⋊ C32
HallC5×C43 ⋊ C22×C32
HallC22×C43 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC22×C3×C5C43⋊C3
commutator, hypocenterC43C22×C32×C5
FrattiniC1G
Fitting, socleC22×C3×C5×C43C3
LCSG ▷ C43
UCSC1 ◁ C22×C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1020 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7740, 118);