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C2×C41×AGL(1,𝔽11) #22583182

order9020
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C22×C5×C41 · Schur multiplier (H2) = C2

Aliases

direct productC2×C41×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C5×C41)
unambiguous semidirect product(C2×D11)⋊(C5×C41)
unambiguous semidirect product(C11⋊C5)⋊(C22×C41)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C41)

Splittings

Fitting, socleC2×C11×C41 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C5×C41
HallC41×C11⋊C5 ⋊ C22
HallC2×D11×C41 ⋊ C5
HallC11×C41 ⋊ C22×C5
HallC11⋊C5 ⋊ C22×C41
HallC2×D11 ⋊ C5×C41

Subgroups

subgroupG/H
center, hypercenterC2×C41AGL(1,𝔽11)
commutator, hypocenterC11C22×C5×C41
FrattiniC1G
Fitting, socleC2×C11×C41C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C41

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

902 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C41×AGL(1,𝔽11), C2×C3×C41×AGL(1,𝔽11), C2×C41×C3⋊AGL(1,𝔽11)
maximal normal subgroup ofC2×C3×C41×AGL(1,𝔽11)
maximal quotient ofD3×C41×AGL(1,𝔽11), C2×C3×C41×AGL(1,𝔽11), C2×C41×C3⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9020, 53);