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C2×C32×AGL(1,𝔽11) #14520442

order1980
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C32×C5)
unambiguous semidirect product(C2×D11)⋊(C32×C5)
unambiguous semidirect product(C11⋊C5)⋊(C22×C32)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C32)
unambiguous semidirect product(C2×C3×D11)⋊(C3×C5)
unambiguous semidirect product(C2×C32×D11)⋊C5

Splittings

Fitting, socleC2×C32×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C32×C5
HallC32×C11⋊C5 ⋊ C22
HallC2×C32×D11 ⋊ C5
HallC32×C11 ⋊ C22×C5
HallC11⋊C5 ⋊ C22×C32
HallC2×D11 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 198

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×AGL(1,𝔽11), C2×C3×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C2×C3×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal normal subgroup ofC2×C32×C7×AGL(1,𝔽11), C2×C32×C11×AGL(1,𝔽11), C2×C32×C13×AGL(1,𝔽11), …
maximal quotient ofC3×AGL(1,𝔽7)×AGL(1,𝔽11), C2×C3×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C2×C3×ΓL(1,𝔽8)×AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 67);