Finite Group Databasebeta

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C3⋊D3×#4869 #72245013

order3456
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC3⋊D3×#4869

Splittings

FittingC33×#106 ⋊ C22
SylowC33 ⋊ C2×#442

Subgroups

subgroupG/H
centerC22D3×D4×C3⋊D3
commutatorC33×C4C23×C4
FrattiniC2×C4C22×D3×C3⋊D3
FittingC33×#106C22
socleC22×C33C22×D4
prime radicalC2×C3⋊D3×D24C2
cosocleC2×C33×C4C24
hypercenter#106D3×C3⋊D3
hypocenterC33C2×#442
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

4176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C3⋊D3×#442
maximal normal subgroup ofD3×C3⋊D3×#442

GAP

Past the SmallGroups library coverage — no SmallGroups id.