Finite Group Databasebeta

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C3×#67×AGL(1,𝔽11) #72247192

order7920
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23

Aliases

direct productC3×#67×AGL(1,𝔽11)

Splittings

FittingC22×C32×C11 ⋊ C22×C5
HallC3×D11×#67 ⋊ C5
HallC32×C11⋊C5 ⋊ C2×D4
HallC32×C11 ⋊ C2×C5×D4
HallC11⋊C5 ⋊ C2×C3×#67
SylowC11 ⋊ C2×C3×C5×#67
SylowC32 ⋊ D4×AGL(1,𝔽11)

Subgroups

subgroupG/H
centerC2×C3C2×D3×AGL(1,𝔽11)
commutator, cosocleC2×C3×C11C23×C3×C5
FrattiniC2C2×C3×D3×AGL(1,𝔽11)
FittingC22×C32×C11C22×C5
socleC2×C32×C11C23×C5
hypercenterC22×C3D3×AGL(1,𝔽11)
hypocenterC3×C11C2×C3×C5×D4
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C2×C3 ◁ C22×C3

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽11)×#3811
maximal normal subgroup ofAGL(1,𝔽11)×#3811

GAP

Past the SmallGroups library coverage — no SmallGroups id.