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C2×C9×AGL(1,𝔽11) #14520390

order1980
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C5×C9)
unambiguous semidirect product(C2×D11)⋊(C5×C9)
unambiguous semidirect product(C11⋊C5)⋊(C22×C9)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C9)
unambiguous semidirect product(C2×C9×D11)⋊C5

Splittings

FittingC2×C9×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C5×C9
HallC9×C11⋊C5 ⋊ C22
HallC2×C9×D11 ⋊ C5
HallC9×C11 ⋊ C22×C5
HallC11⋊C5 ⋊ C22×C9
HallC2×D11 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9AGL(1,𝔽11)
commutator, hypocenterC11C22×C5×C9
FrattiniC3C2×C3×AGL(1,𝔽11)
FittingC2×C9×C11C2×C5
socleC2×C3×C11C2×C3×C5
prime radicalC2×C3×AGL(1,𝔽11)C3
cosocleC3×C11C22×C3×C5
LCSG ▷ C11
UCSC1 ◁ C2×C9

60 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 ofAGL(1,𝔽11)×D7⋊C9, C2×(C11⋊C5)⋊(D7⋊C9), C2×C7⋊C9×AGL(1,𝔽11), …
maximal normal subgroup ofC2×C7×C9×AGL(1,𝔽11), C2×C9×C11×AGL(1,𝔽11), C2×C9×C13×AGL(1,𝔽11), …
maximal quotient ofAGL(1,𝔽11)×D7⋊C9, C2×(C11⋊C5)⋊(D7⋊C9), C2×C7⋊C9×AGL(1,𝔽11), …
automorphism group ofC19×D11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 15);