Finite Group Databasebeta

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D3×#24260 #72270972

order1536
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productD3×#24260

Splittings

FittingC3×#24260 ⋊ C2
SylowC3 ⋊ C2×#24260

Subgroups

subgroupG/H
centerC22C2×D3×#120
commutator, cosocleC24×C3C25
FrattiniC24C24×D3
FittingC3×#24260C2
socleC22×C3C22×#120
hypercenter#24260D3
hypocenterC3C2×#24260
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #24260

13428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D4×B(4,𝔽2), D3×#6512843, D3×#6454041, …
maximal normal subgroup ofD3×D4×B(4,𝔽2), D3×#6512843, D3×#6454041, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.