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C2×C43×AGL(1,𝔽11) #22628186

order9460
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C22×C5×C43 · Schur multiplier (H2) = C2

Aliases

direct productC2×C43×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C5×C43)
unambiguous semidirect product(C2×D11)⋊(C5×C43)
unambiguous semidirect product(C11⋊C5)⋊(C22×C43)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C43)
unambiguous semidirect product(C2×D11×C43)⋊C5

Splittings

Fitting, socleC2×C11×C43 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C5×C43
HallC43×C11⋊C5 ⋊ C22
HallC2×D11×C43 ⋊ C5
HallC11×C43 ⋊ C22×C5
HallC11⋊C5 ⋊ C22×C43
HallC2×D11 ⋊ C5×C43

Subgroups

subgroupG/H
center, hypercenterC2×C43AGL(1,𝔽11)
commutator, hypocenterC11C22×C5×C43
FrattiniC1G
Fitting, socleC2×C11×C43C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C43

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

946 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽11)×C43⋊C3, D3×C43×AGL(1,𝔽11), C2×C3×C43×AGL(1,𝔽11), …
maximal normal subgroup ofC2×AGL(1,𝔽11)×C43⋊C3, C2×C3×C43×AGL(1,𝔽11)
maximal quotient ofD3×C43×AGL(1,𝔽11), C2×C3×C43×AGL(1,𝔽11), C2×C43×C3⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9460, 15);