Finite Group Databasebeta

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#492×AGL(1,𝔽11) #72248941

order7040
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24×C4

Aliases

direct product#492×AGL(1,𝔽11)

Splittings

FittingC11×#492 ⋊ C2×C5
HallD11×#492 ⋊ C5
HallC11⋊C5 ⋊ C2×#492
SylowC11 ⋊ C2×C5×#492

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,𝔽11)
commutator, cosocleC2×C4×C11C24×C5
FrattiniC2×C4C23×AGL(1,𝔽11)
FittingC11×#492C2×C5
socleC22×C11C22×C5×D4
prime radical#127×AGL(1,𝔽11)C2
hypercenter#492AGL(1,𝔽11)
hypocenterC11C2×C5×#492
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #492

1312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

242 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×#3151, AGL(1,𝔽11)×#1715, AGL(1,𝔽11)×#1721, …
maximal normal subgroup ofAGL(1,𝔽11)×#3151, AGL(1,𝔽11)×#1715, AGL(1,𝔽11)×#1721, …
maximal quotient ofAGL(1,𝔽11)×#1715, AGL(1,𝔽11)×#1705

GAP

Past the SmallGroups library coverage — no SmallGroups id.