Finite Group Databasebeta

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C3×A4×#235 #13181438

order1728
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3

Aliases

direct productC3×A4×#235
unambiguous semidirect product(C22×#235)⋊C32
unambiguous semidirect product(C22×C3×#235)⋊C3

Splittings

FittingC23×C32×C4 ⋊ C2×C3

Subgroups

subgroupG/H
centerC3×C4C2×D3×A4
commutator, cosocleC23×C3C23×C32
FrattiniC2C22×C3×D3×A4
FittingC23×C32×C4C2×C3
socleC23×C32C23×C3
hypercenterC2×C3×C4D3×A4
hypocenterC22×C3C32×#41
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47501);