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C22×C22⋊AGL(1,𝔽11) #13183291

order1760
isoclinismisoclinic class of (C11⋊C5)⋊Q8
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC22×C22⋊AGL(1,𝔽11)
unambiguous semidirect product(C22×C22⋊D11)⋊C5

Splittings

FittingC24×C11 ⋊ C2×C5
HallC22×C22⋊D11 ⋊ C5
HallC11⋊C5 ⋊ C22×D4
SylowC11 ⋊ C22×C5×D4

Subgroups

subgroupG/H
centerC23C2×AGL(1,𝔽11)
commutator, cosocleC2×C11C24×C5
FrattiniC2C23×AGL(1,𝔽11)
FittingC24×C11C2×C5
socleC23×C11C22×C5
hypercenterC24AGL(1,𝔽11)
hypocenterC11C22×C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×D4×AGL(1,𝔽11), C2×#66990⋊C5, C2×#66935⋊C5, …
maximal normal subgroup ofC22×D4×AGL(1,𝔽11), C2×#66990⋊C5, C2×#66935⋊C5, …
maximal quotient ofC2×#66990⋊C5, C2×#67006⋊C5, C2×D3×C22⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1100);