Finite Group Databasebeta

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C3×#11703805 #72215292

order2304
automorphism?
homologyAbelianization (H1) = C26×C3 · Schur multiplier (H2) = C213

Aliases

direct productC3×#11703805

Splittings

FittingC22×C32×#120 ⋊ C2
SylowC32 ⋊ #62817

Subgroups

subgroupG/H
centerC22×C3C25×D3
commutator, cosocleC22×C3C26×C3
FrattiniC22C25×C3×D3
FittingC22×C32×#120C2
socleC22×C32C26
hypercenterC22×C3×#120D3
hypocenterC3C3×#62817
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×#120

21260 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

396 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×#72252298, C3×#72231563
maximal normal subgroup ofC3×#72252298, C3×#72231563

GAP

Past the SmallGroups library coverage — no SmallGroups id.