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C2×C8×AGL(1,𝔽11) #13182500

order1760
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×C8×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C5×C8)
unambiguous semidirect product(C2×C8×D11)⋊C5

Splittings

FittingC2×C8×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C5×C8
HallC2×C8×D11 ⋊ C5
HallC11⋊C5 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8AGL(1,𝔽11)
commutator, hypocenterC11C22×C5×C8
FrattiniC4C22×AGL(1,𝔽11)
FittingC2×C8×C11C2×C5
socleC22×C11C2×C4×C5
prime radicalC22×AGL(1,𝔽11)C4
cosocleC4×C11C23×C5
LCSG ▷ C11
UCSC1 ◁ C2×C8

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C8×AGL(1,𝔽11), C2×M16×AGL(1,𝔽11), C2×D8×AGL(1,𝔽11), …
maximal normal subgroup ofC2×M16×AGL(1,𝔽11), C2×D8×AGL(1,𝔽11), C2×SD16×AGL(1,𝔽11), …
maximal quotient ofD3×C8×AGL(1,𝔽11), M32×AGL(1,𝔽11), C4×C8×AGL(1,𝔽11)
automorphism group ofC11⋊C32

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 309);