Finite Group Databasebeta

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C3×#11701722 #72222751

order2304
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29

Aliases

direct productC3×#11701722

Splittings

FittingC2×C32×#509 ⋊ C2
SylowC32 ⋊ #62636

Subgroups

subgroupG/H
centerC2×C3C22×D3×D8
commutator, cosocleC3×C8C25×C3
FrattiniC8C24×C3×D3
FittingC2×C32×#509C2
socleC2×C32C23×D8
hypercenterC2×C3×#509D3
hypocenterC3C3×#62636
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×#509

4356 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×#72228227
maximal normal subgroup ofC3×#72228227

GAP

Past the SmallGroups library coverage — no SmallGroups id.