Finite Group Databasebeta

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D3×#21408 #72270012

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productD3×#21408

Splittings

FittingC3×#21408 ⋊ C2
SylowC3 ⋊ C2×#21408

Subgroups

subgroupG/H
centerC23C22×D3×D4
commutatorC2×C3×C4C24×C4
FrattiniC22×C4C24×D3
FittingC3×#21408C2
socleC23×C3C23×D4
prime radicalC2×D3×#532C2
cosocleC22×C3×C4C25
hypercenter#21408D3
hypocenterC3C2×#21408
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C42 ◁ #21408

9780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

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×#495573

GAP

Past the SmallGroups library coverage — no SmallGroups id.