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C2×C3×C3⋊AGL(1,𝔽11) #14520444

order1980
isoclinismisoclinic class of C3⋊AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C3)⋊(C3×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C3×D3)
unambiguous semidirect product(C2×D33)⋊(C3×C5)
unambiguous semidirect product(C2×C3×D33)⋊C5

Splittings

Fitting, socleC2×C32×C11 ⋊ C2×C5
derivedC3×C11 ⋊ C22×C3×C5
HallC32×C11⋊C5 ⋊ C22
HallC2×C3×D33 ⋊ C5
HallC32×C11 ⋊ C22×C5
HallC11⋊C5 ⋊ C2×C3×D3
SylowC11 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C2×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C11C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×C3⋊AGL(1,𝔽11), C2×C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11)), C2×ΓL(1,𝔽8)×C3⋊AGL(1,𝔽11), …
maximal normal subgroup ofC2×C3×C7×C3⋊AGL(1,𝔽11), C2×C3×C11×C3⋊AGL(1,𝔽11), C2×C3×C13×C3⋊AGL(1,𝔽11), …
maximal quotient ofAGL(1,𝔽7)×C3⋊AGL(1,𝔽11), C2×C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11)), C2×ΓL(1,𝔽8)×C3⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 69);