Finite Group Databasebeta

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#322×AGL(1,𝔽11) #72249018

order7040
automorphism?
homologyAbelianization (H1) = C2×C4×C5×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#322×AGL(1,𝔽11)

Splittings

FittingC11×#322 ⋊ C2×C5
HallD11×#322 ⋊ C5
HallC11⋊C5 ⋊ C2×#322
SylowC11 ⋊ C2×C5×#322

Subgroups

subgroupG/H
center, FrattiniC42C22×AGL(1,𝔽11)
commutatorC2×C11C2×C4×C5×C8
FittingC11×#322C2×C5
socleC22×C11C2×C42×C5
prime radicalC22×AGL(1,𝔽11)C42
cosocleC42×C11C23×C5
hypercenter#322AGL(1,𝔽11)
hypocenterC11C2×C5×#322
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ #322

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽11)×#1715, AGL(1,𝔽11)×#1721, AGL(1,𝔽11)×#1455
maximal normal subgroup ofAGL(1,𝔽11)×#1715, AGL(1,𝔽11)×#1721, AGL(1,𝔽11)×#1455

GAP

Past the SmallGroups library coverage — no SmallGroups id.