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B(4,𝔽2)×GO+(4,𝔽2) #72253221

order4608
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productB(4,𝔽2)×GO+(4,𝔽2)

Splittings

FittingC32×B(4,𝔽2) ⋊ D4
SylowC32 ⋊ D4×B(4,𝔽2)

Subgroups

subgroupG/H
centerC2#120×GO+(4,𝔽2)
commutator, cosocleC23×C3⋊D3C25
FrattiniC23C23×GO+(4,𝔽2)
FittingC32×B(4,𝔽2)D4
socleC2×C32D4×#120
hypercenterB(4,𝔽2)GO+(4,𝔽2)
hypocenterC32D4×B(4,𝔽2)
LCSG ▷ C23×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ B(4,𝔽2)

20492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofB(4,𝔽2)×AΓL(1,𝔽9)
maximal normal subgroup ofB(4,𝔽2)×AΓL(1,𝔽9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.