Finite Group Databasebeta

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D3×#62811 #72253955

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

Aliases

direct productD3×#62811

Splittings

FittingC3×#62811 ⋊ C2
SylowC3 ⋊ C2×#62811

Subgroups

subgroupG/H
centerC2×C4C25×D3
commutator, socle, cosocleC22×C3C27
FrattiniC22C26×D3
FittingC3×#62811C2
hypercenter#62811D3
hypocenterC3C2×#62811
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #62811

118292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×#10576108, D3×#6437475, D3×#6437616, …
maximal normal subgroup ofD3×#10576108, D3×#6437475, D3×#6437616, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.