Finite Group Databasebeta

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D3×#62842 #72253426

order1536
automorphism?
homologyAbelianization (H1) = C27 · Schur multiplier (H2) = C220

Aliases

direct productD3×#62842

Splittings

FittingC3×#62842 ⋊ C2
SylowC3 ⋊ C2×#62842

Subgroups

subgroupG/H
center, FrattiniC22C26×D3
commutator, socle, cosocleC22×C3C27
FittingC3×#62842C2
hypercenter#62842D3
hypocenterC3C2×#62842
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #62842

120244 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#6437576, D3×#6431795, D3×#6437632
maximal normal subgroup ofD3×#6437576, D3×#6431795, D3×#6437632
maximal quotient ofD3×#7631286, D3×#7918389, D3×#7695992

GAP

Past the SmallGroups library coverage — no SmallGroups id.