Finite Group Databasebeta

← Prev (#72228719) Next (#72228721) →

3−1+2×AGL(1,𝔽11) #72228720

order2970
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C1

Aliases

direct product3−1+2×AGL(1,𝔽11)

Splittings

Fitting, HallC11×3−1+2 ⋊ C2×C5
Hall3−1+2×C11⋊C5 ⋊ C2
HallD11×3−1+2 ⋊ C5
HallC11⋊C5 ⋊ C2×3−1+2
HallD11 ⋊ C5×3−1+2
SylowC11 ⋊ C2×C5×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×AGL(1,𝔽11)
commutator, socle, cosocleC3×C11C2×C32×C5
FittingC11×3−1+2C2×C5
prime radicalC32×AGL(1,𝔽11)C3
hypercenter3−1+2AGL(1,𝔽11)
hypocenterC11C2×C5×3−1+2
LCSG ▷ C3×C11 ▷ C11
UCSC1 ◁ C3 ◁ 3−1+2

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 99

A minimal faithful permutation representation — 2 generators on 20 points:

(2,4,7)(5,9,8)(11,14,15,19,18,12,13,16,17,20);(1,2,5,6,7,9,3,4,8)(10,11,14,17,15,18,20,16,19,13,12)

Conjugacy classes & character table

121 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/9)×AGL(1,𝔽11), C2×3−1+2×AGL(1,𝔽11)
maximal normal subgroup ofAGL(1,ℤ/9)×AGL(1,𝔽11), C2×3−1+2×AGL(1,𝔽11)
maximal quotient ofC2×3−1+2×AGL(1,𝔽11)

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((2,4,7)(5,9,8)(11,14,15,19,18,12,13,16,17,20), (1,2,5,6,7,9,3,4,8)(10,11,14,17,15,18,20,16,19,13,12));