Finite Group Databasebeta

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D3×#39358 #72270680

order1536
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productD3×#39358

Splittings

FittingC3×#39358 ⋊ C2
SylowC3 ⋊ C2×#39358

Subgroups

subgroupG/H
center, FrattiniC23C25×D3
commutator, socle, cosocleC23×C3C26
FittingC3×#39358C2
hypercenter#39358D3
hypocenterC3C2×#39358
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #39358

30188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#7695992, D3×#7659307
maximal normal subgroup ofD3×#7695992, D3×#7659307
maximal quotient ofD3×#687584, D3×#772785

GAP

Past the SmallGroups library coverage — no SmallGroups id.