Finite Group Databasebeta

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D3×#32878 #72253273

order1536
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C213

Aliases

direct productD3×#32878

Splittings

FittingC3×#32878 ⋊ C2
SylowC3 ⋊ C2×#32878

Subgroups

subgroupG/H
centerC23C22×D3×D4
commutator, cosocleC22×C3×C4C25
FrattiniC22×C4C24×D3
FittingC3×#32878C2
socleC23×C3C23×D4
hypercenter#32878D3
hypocenterC3C2×#32878
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ #32878

60168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#6628842
maximal normal subgroup ofD3×#6628842

GAP

Past the SmallGroups library coverage — no SmallGroups id.