Finite Group Databasebeta

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AGL(1,𝔽11)×#1455 #72254653

order14080
automorphism?
homologyAbelianization (H1) = C22×C42×C5 · Schur multiplier (H2) = C23×C8

Aliases

direct productAGL(1,𝔽11)×#1455

Splittings

FittingC11×#1455 ⋊ C2×C5
HallD11×#1455 ⋊ C5
HallC11⋊C5 ⋊ C2×#1455
SylowC11 ⋊ C2×C5×#1455

Subgroups

subgroupG/H
center, FrattiniC42C23×AGL(1,𝔽11)
commutator, socleC22×C11C22×C42×C5
FittingC11×#1455C2×C5
prime radicalC23×AGL(1,𝔽11)C42
cosocleC42×C11C24×C5
hypercenter#1455AGL(1,𝔽11)
hypocenterC11C2×C5×#1455
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C42 ◁ #1455

1988 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

Relationships

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.