Finite Group Databasebeta

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D3×#21379 #72270030

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD3×#21379

Splittings

FittingC3×#21379 ⋊ C2
SylowC3 ⋊ C2×#21379

Subgroups

subgroupG/H
center, FrattiniC22×C4C24×D3
commutator, socleC23×C3C24×C4
FittingC3×#21379C2
prime radicalC22×D3×#41C4
cosocleC22×C3×C4C25
hypercenter#21379D3
hypocenterC3C2×#21379
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #21379

9732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#6453969
maximal normal subgroup ofD3×#6453969
maximal quotient ofD3×#495505

GAP

Past the SmallGroups library coverage — no SmallGroups id.