Finite Group Databasebeta

← Prev (#72259240) Next (#72259242) →

B(4,𝔽2)×AGL(1,𝔽13) #72259241

order9984
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27

Aliases

direct productB(4,𝔽2)×AGL(1,𝔽13)

Splittings

FittingC13×B(4,𝔽2) ⋊ C3×C4
Hall#261×B(4,𝔽2) ⋊ C3
HallC13⋊C3 ⋊ C4×B(4,𝔽2)
SylowC13 ⋊ C3×C4×B(4,𝔽2)

Subgroups

subgroupG/H
centerC2#120×AGL(1,𝔽13)
commutatorC23×C13C23×C3×C4
FrattiniC23C23×AGL(1,𝔽13)
FittingC13×B(4,𝔽2)C3×C4
socleC2×C13C3×C4×#120
prime radicalB(4,𝔽2)×D13⋊C3C2
cosocleC23×D13C24×C3
hypercenterB(4,𝔽2)AGL(1,𝔽13)
hypocenterC13C3×C4×B(4,𝔽2)
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ B(4,𝔽2)

3820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 104

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽13)×#5934
automorphism group ofC2×Dic26, C2×D52
holomorph ofC2×C4×C13

GAP

Past the SmallGroups library coverage — no SmallGroups id.