Finite Group Databasebeta

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AGL(1,𝔽11)×#3811 #72247252

order15840
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productAGL(1,𝔽11)×#3811

Splittings

FittingC22×C32×C11 ⋊ C23×C5
HallD11×#3811 ⋊ C5
HallC32×C11⋊C5 ⋊ C22×D4
HallC32×C11 ⋊ C22×C5×D4
HallC11⋊C5 ⋊ C2×#3811
SylowC11 ⋊ C2×C5×#3811
SylowC32 ⋊ C2×D4×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, FrattiniC2C2×D32×AGL(1,𝔽11)
commutator, socle, cosocleC2×C32×C11C24×C5
FittingC22×C32×C11C23×C5
hypercenterC22D32×AGL(1,𝔽11)
hypocenterC32×C11C22×C5×D4
LCSG ▷ C2×C32×C11 ▷ C32×C11
UCSC1 ◁ C2 ◁ C22

2156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

Relationships

holomorph ofC11×Dic3, C2×D3×C11

GAP

Past the SmallGroups library coverage — no SmallGroups id.