Finite Group Databasebeta

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#360×AGL(1,𝔽11) #72248773

order7040
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct product#360×AGL(1,𝔽11)

Splittings

FittingC11×#360 ⋊ C2×C5
HallD11×#360 ⋊ C5
HallC11⋊C5 ⋊ C2×#360
SylowC11 ⋊ C2×C5×#360

Subgroups

subgroupG/H
centerC2#102×AGL(1,𝔽11)
commutatorC8×C11C22×C4×C5
FrattiniC2×C8C22×AGL(1,𝔽11)
FittingC11×#360C2×C5
socleC2×C11C2×C5×#102
prime radical#135×AGL(1,𝔽11)C2
cosocleC2×C8×C11C23×C5
hypercenter#360AGL(1,𝔽11)
hypocenterC11C2×C5×#360
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×AGL(1,ℤ/16)
maximal normal subgroup ofAGL(1,𝔽11)×AGL(1,ℤ/16)

GAP

Past the SmallGroups library coverage — no SmallGroups id.