Finite Group Databasebeta

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D3×#60444 #72253959

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

Aliases

direct productD3×#60444

Splittings

FittingC3×#60444 ⋊ C2
SylowC3 ⋊ C2×#60444

Subgroups

subgroupG/H
centerC2×C4C22×D3×D4
commutator, cosocleC2×C3×C4C26
FrattiniC2×C4C25×D3
FittingC3×#60444C2
socleC22×C3C24×D4
hypercenter#60444D3
hypocenterC3C2×#60444
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #60444

22708 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#394321, D3×#10576108, D3×#394195
maximal normal subgroup ofD3×#394321, D3×#10576108, D3×#394195

GAP

Past the SmallGroups library coverage — no SmallGroups id.