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B(4,𝔽2)×#1035 #72275700

order6400
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productB(4,𝔽2)×#1035

Splittings

FittingC25×B(4,𝔽2) ⋊ C4
SylowC25 ⋊ C4×B(4,𝔽2)

Subgroups

subgroupG/H
centerC2#120×#1035
commutatorC23×C25C23×C4
FrattiniC23×C5C23×AGL(1,𝔽5)
FittingC25×B(4,𝔽2)C4
socleC2×C5AGL(1,𝔽5)×#120
prime radicalD25×B(4,𝔽2)C2
cosocleC23×D25C24
hypercenterB(4,𝔽2)#1035
hypocenterC25C4×B(4,𝔽2)
LCSG ▷ C23×C25 ▷ C2×C25 ▷ C25
UCSC1 ◁ C2 ◁ C23 ◁ B(4,𝔽2)

2865 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofB(4,𝔽2)×AGL(1,ℤ/25)
maximal normal subgroup ofB(4,𝔽2)×AGL(1,ℤ/25)

GAP

Past the SmallGroups library coverage — no SmallGroups id.