Finite Group Databasebeta

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D3×#32888 #72252261

order1536
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C212

Aliases

direct productD3×#32888

Splittings

FittingC3×#32888 ⋊ C2
SylowC3 ⋊ C2×#32888

Subgroups

subgroupG/H
centerC22C2×D3×#120
commutator, cosocleC22×C3×C4C25
FrattiniC22×C4C24×D3
FittingC3×#32888C2
socleC22×C3C22×#120
hypercenter#32888D3
hypocenterC3C2×#32888
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #32888

37768 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72252285, D3×#6628867
maximal normal subgroup ofD3×#6628867
maximal quotient of#72252285, D3×#346446

GAP

Past the SmallGroups library coverage — no SmallGroups id.