Finite Group Databasebeta

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D3×#36702 #72248141

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

Aliases

direct productD3×#36702

Splittings

FittingC3×#36702 ⋊ C2
SylowC3 ⋊ C2×#36702

Subgroups

subgroupG/H
center, FrattiniC23C25×D3
commutator, socle, cosocleC23×C3C26
FittingC3×#36702C2
hypercenter#36702D3
hypocenterC3C2×#36702
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #36702

35084 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#147811, D3×#7792761, D3×#498927, …
maximal normal subgroup ofD3×#147811, D3×#7792761, D3×#498927, …
maximal quotient ofD3×#846041, D3×#4312024

GAP

Past the SmallGroups library coverage — no SmallGroups id.