Finite Group Databasebeta

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D3×#21793 #72271109

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C42

Aliases

direct productD3×#21793

Splittings

FittingC3×#21793 ⋊ C2
SylowC3 ⋊ C2×#21793

Subgroups

subgroupG/H
centerC22C22×D3×C22⋊C4
commutatorC23×C3C24×C4
FrattiniC24C24×D3
FittingC3×#21793C2
socleC22×C3C23×C22⋊C4
prime radicalC22×D3×#121C2
cosocleC24×C3C25
hypercenter#21793D3
hypocenterC3C2×#21793
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24×C4 ◁ #21793

13588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#6512843
maximal normal subgroup ofD3×#6512843

GAP

Past the SmallGroups library coverage — no SmallGroups id.