Finite Group Databasebeta

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D12×B(4,𝔽2) #72270977

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

Aliases

direct productD12×B(4,𝔽2)

Splittings

FittingC3×C4×B(4,𝔽2) ⋊ C2
SylowC3 ⋊ D4×B(4,𝔽2)

Subgroups

subgroupG/H
centerC22C2×D3×#120
commutator, cosocleC24×C3C25
FrattiniC24C24×D3
FittingC3×C4×B(4,𝔽2)C2
socleC22×C3C22×#120
hypercenterC4×B(4,𝔽2)D3
hypocenterC3D4×B(4,𝔽2)
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×B(4,𝔽2)

13478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D4×B(4,𝔽2), #72271270, #72271836
maximal normal subgroup ofD3×D4×B(4,𝔽2), #72271270, #72271836

GAP

Past the SmallGroups library coverage — no SmallGroups id.