Finite Group Databasebeta

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D3×#21452 #72219851

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

Aliases

direct productD3×#21452

Splittings

FittingC3×#21452 ⋊ C2
SylowC3 ⋊ C2×#21452

Subgroups

subgroupG/H
centerC23C22×D3×D4
commutatorC2×C3×C4C24×C4
FrattiniC22×C4C24×D3
FittingC3×#21452C2
socleC23×C3C23×D4
prime radicalC2×D3×#447C2
cosocleC22×C3×C4C25
hypercenter#21452D3
hypocenterC3C2×#21452
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C42 ◁ #21452

14196 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#6453969
maximal normal subgroup ofD3×#6453969
maximal quotient ofD3×#495725, D3×#495739

GAP

Past the SmallGroups library coverage — no SmallGroups id.