Finite Group Databasebeta

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D3×#10737 #72249284

order1536
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C29

Aliases

direct productD3×#10737

Splittings

FittingC3×#10737 ⋊ C2
SylowC3 ⋊ C2×#10737

Subgroups

subgroupG/H
centerC2×C4C2×D3×C22⋊C4
commutatorC23×C3C22×C42
FrattiniC23×C4C23×D3
FittingC3×#10737C2
socleC22×C3C22×#95
prime radicalC25×D3C2×C4
cosocleC23×C3×C4C24
hypercenter#10737D3
hypocenterC3C2×#10737
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #10737

9348 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×#374114, D3×#394040, D3×#364416, …
maximal normal subgroup ofD3×#374114, D3×#394040, D3×#364416, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.