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C2×C11×AGL(1,ℤ/9) #11924685

order1188
isoclinismisoclinic class of AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C2×C3×C11)
unambiguous semidirect product3−1+2⋊(C22×C11)
unambiguous semidirect product(C2×D9)⋊(C3×C11)
unambiguous semidirect product(C2×3−1+2)⋊(C2×C11)
unambiguous semidirect product(C2×C11×D9)⋊C3

Splittings

FittingC2×C11×3−1+2 ⋊ C2
derivedC9 ⋊ C22×C3×C11
HallC11×3−1+2 ⋊ C22
Sylow3−1+2 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11AGL(1,ℤ/9)
commutator, cosocle, hypocenterC9C22×C3×C11
FrattiniC3C2×C3×D3×C11
FittingC2×C11×3−1+2C2
socleC2×C3×C11C3×D3
LCSG ▷ C9
UCSC1 ◁ C2×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 198

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D11×AGL(1,ℤ/9), C2×AGL(1,ℤ/9)×C11⋊C5, AGL(1,ℤ/9)×AGL(1,𝔽23)
maximal normal subgroup ofC2×D11×AGL(1,ℤ/9), C2×AGL(1,ℤ/9)×C11⋊C5
maximal quotient ofAGL(1,ℤ/9)×AGL(1,𝔽23)
automorphism group ofD9×C23

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1188, 55);