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SL(2,𝔽11) #13050309

order1320
isoclinismisoclinic class of SL(2,𝔽11)
automorphismAut(G) = PGL(2,𝔽11) (order 1320) · Inn(G) = PSL(2,𝔽11) · Out(G) = C2
homologyAbelianization (H1) = C1 · Schur multiplier (H2) = C1

Aliases

special linearSL(2,𝔽11)
symplecticSp(2,𝔽11)
special unitarySU(2,𝔽11)

Subgroups

subgroupG/H
center, Frattini, Fitting, socle, cosocle, hypercenterC2PSL(2,𝔽11)
commutator, hypocenterGC1
LCSG
UCSC1 ◁ C2

21 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 24

Permutation generators:

(1,2,4,5)(3,6,7,9)(8,10,12,14)(11,15,16,20)(13,17,19,22)(18,21,23,24);(1,3,2)(4,7,5)(6,8,11)(9,12,16)(10,13,18)(14,19,23)(15,17,21)(20,22,24);(1,4)(2,5)(3,7)(6,9)(8,12)(10,14)(11,16)(13,19)(15,20)(17,22)(18,23)(21,24)

Conjugacy classes & character table

15 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×SL(2,𝔽11), #72210865, C3×SL(2,𝔽11), …
maximal normal subgroup ofC5×SL(2,𝔽11), #72210865, C3×SL(2,𝔽11), …
maximal quotient ofC5×SL(2,𝔽11), C3×SL(2,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 13);