Finite Group Databasebeta

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D3×#60372 #72272154

order1536
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C215

Aliases

direct productD3×#60372

Splittings

FittingC3×#60372 ⋊ C2
SylowC3 ⋊ C2×#60372

Subgroups

subgroupG/H
centerC22C23×D3×D4
commutator, cosocleC2×C3×C4C26
FrattiniC2×C4C25×D3
FittingC3×#60372C2
socleC22×C3C24×D4
hypercenter#60372D3
hypocenterC3C2×#60372
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×#41 ◁ #60372

47272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

183 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#10574840
maximal normal subgroup ofD3×#10574840

GAP

Past the SmallGroups library coverage — no SmallGroups id.