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C3×C22⋊AGL(1,𝔽11) #13050323

order1320
isoclinismisoclinic class of (C11⋊C5)⋊Q8
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C22⋊AGL(1,𝔽11)
unambiguous semidirect product(C22⋊D11)⋊(C3×C5)
unambiguous semidirect product(C3×C22⋊D11)⋊C5

Splittings

FittingC22×C3×C11 ⋊ C2×C5
HallC3×C22⋊D11 ⋊ C5
HallC3×C11⋊C5 ⋊ D4
HallC22⋊D11 ⋊ C3×C5
HallC11⋊C5 ⋊ C3×D4
HallC3×C11 ⋊ C5×D4
SylowC11 ⋊ C3×C5×D4

Subgroups

subgroupG/H
centerC2×C3C2×AGL(1,𝔽11)
commutator, cosocleC2×C11C22×C3×C5
FrattiniC2C2×C3×AGL(1,𝔽11)
FittingC22×C3×C11C2×C5
socleC2×C3×C11C22×C5
hypercenterC22×C3AGL(1,𝔽11)
hypocenterC11C3×C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C3 ◁ C22×C3

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 132

A minimal faithful permutation representation — 2 generators on 18 points:

(1,2,3)(4,5,6,11,14)(7,12,8,13,10)(16,18);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18)

Conjugacy classes & character table

87 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D4×AGL(1,𝔽11), D3×C22⋊AGL(1,𝔽11), #72216761, …
maximal normal subgroup ofC3×D4×AGL(1,𝔽11), D3×C22⋊AGL(1,𝔽11), #72216761, …
maximal quotient ofC2×C3×C22⋊AGL(1,𝔽11), C3×#4323⋊C5, C3×#4324⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 27);