Finite Group Databasebeta

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AGL(1,𝔽11)×#3151 #72249000

order14080
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C28×C4

Aliases

direct productAGL(1,𝔽11)×#3151

Splittings

FittingC11×#3151 ⋊ C2×C5
HallD11×#3151 ⋊ C5
HallC11⋊C5 ⋊ C2×#3151
SylowC11 ⋊ C2×C5×#3151

Subgroups

subgroupG/H
centerC22C22×D4×AGL(1,𝔽11)
commutator, cosocleC2×C4×C11C25×C5
FrattiniC2×C4C24×AGL(1,𝔽11)
FittingC11×#3151C2×C5
socleC22×C11C23×C5×D4
hypercenter#3151AGL(1,𝔽11)
hypocenterC11C2×C5×#3151
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3151

7900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽11)×#19745
maximal normal subgroup ofAGL(1,𝔽11)×#19745
maximal quotient ofAGL(1,𝔽11)×#19745

GAP

Past the SmallGroups library coverage — no SmallGroups id.