Finite Group Databasebeta

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C32×D3×#442 #72245115

order3456
automorphism?
homologyAbelianization (H1) = C23×C32×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC32×D3×#442

Splittings

FittingC33×#442 ⋊ C2
SylowC33 ⋊ C2×#442

Subgroups

subgroupG/H
centerC22×C32C2×D3×D4
commutatorC3×C4C23×C32×C4
FrattiniC2×C4C23×C32×D3
FittingC33×#442C2
socleC22×C33C22×D4
prime radicalC2×C32×D3×D8C2
cosocleC2×C3×C4C24×C32
hypercenterC32×#442D3
hypocenterC3C2×C32×#442
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×C42 ◁ C32×#442

4176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

Relationships

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.