Finite Group Databasebeta

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D3×#10965 #72247715

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C210

Aliases

direct productD3×#10965

Splittings

FittingC3×#10965 ⋊ C2
SylowC3 ⋊ C2×#10965

Subgroups

subgroupG/H
centerC23C2×D3×C22⋊C4
commutatorC24×C3C23×C4
FrattiniC25C23×D3
FittingC3×#10965C2
socleC23×C3C22×C22⋊C4
prime radicalC22×D3×#120C2
cosocleC25×C3C24
hypercenter#10965D3
hypocenterC3C2×#10965
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C26 ◁ #10965

26540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#394066, D3×#449475, D3×#417824, …
maximal normal subgroup ofD3×#394066, D3×#449475, D3×#417824, …
maximal quotient ofD3×#147555, D3×#115690, D3×#147567, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.