Finite Group Databasebeta

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D3×#21005 #72253370

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productD3×#21005

Splittings

FittingC3×#21005 ⋊ C2
SylowC3 ⋊ C2×#21005

Subgroups

subgroupG/H
centerC22C2×D3×#121
commutatorC2×C3×C4C24×C4
FrattiniC22×C4C24×D3
FittingC3×#21005C2
socleC22×C3C22×#121
prime radicalC22×D3×AGL(1,ℤ/8)C2
cosocleC22×C3×C4C25
hypercenter#21005D3
hypocenterC3C2×#21005
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #21005

13140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#418876, D3×#383145, D3×#6437793
maximal normal subgroup ofD3×#418876, D3×#383145, D3×#6437793

GAP

Past the SmallGroups library coverage — no SmallGroups id.