Finite Group Databasebeta

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C3×D3×#3151 #72243457

order2304
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C28×C4

Aliases

direct productC3×D3×#3151

Splittings

FittingC32×#3151 ⋊ C2
SylowC32 ⋊ C2×#3151

Subgroups

subgroupG/H
centerC22×C3C22×D3×D4
commutator, cosocleC2×C3×C4C25×C3
FrattiniC2×C4C24×C3×D3
FittingC32×#3151C2
socleC22×C32C23×D4
hypercenterC3×#3151D3
hypocenterC3C2×C3×#3151
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#3151

8228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,ℤ/9)×#3151, C3×D3×#19745, D32×#3151
maximal normal subgroup ofC3×D3×#19745, D32×#3151
maximal quotient ofAGL(1,ℤ/9)×#3151, C3×D3×#19745

GAP

Past the SmallGroups library coverage — no SmallGroups id.