Finite Group Databasebeta

← Prev (#72248795) Next (#72248797) →

AGL(1,𝔽11)×AGL(1,ℤ/16) #72248796

order14080
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽11)×AGL(1,ℤ/16)

Splittings

FittingC11×AGL(1,ℤ/16) ⋊ C2×C5
HallD11×AGL(1,ℤ/16) ⋊ C5
HallC11⋊C5 ⋊ C2×AGL(1,ℤ/16)
SylowC11 ⋊ C2×C5×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC2#442×AGL(1,𝔽11)
commutatorC8×C11C23×C4×C5
FrattiniC2×C8C23×AGL(1,𝔽11)
FittingC11×AGL(1,ℤ/16)C2×C5
socleC2×C11C2×C5×#442
prime radical#509×AGL(1,𝔽11)C2
cosocleC2×C8×C11C24×C5
hypercenterAGL(1,ℤ/16)AGL(1,𝔽11)
hypocenterC11C2×C5×AGL(1,ℤ/16)
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

1420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

253 conjugacy classes — view the full character table.

Relationships

holomorph ofC11×C16

GAP

Past the SmallGroups library coverage — no SmallGroups id.