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PSL(2,𝔽23) #72209616

order6072
isoclinismisoclinic class of PSL(2,𝔽23)
automorphismAut(G) = PGL(2,𝔽23) (order 12144) · Inn(G) = G · Out(G) = C2
homologyAbelianization (H1) = C1 · Schur multiplier (H2) = C2

Aliases

projective special linearPSL(2,𝔽23)
projective symplecticPSp(2,𝔽23)
projective special unitaryPSU(2,𝔽23)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, hypocenterGC1
LCSG
UCSC1

23 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

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

Conjugacy classes & character table

14 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofPGL(2,𝔽23)
maximal normal subgroup ofPGL(2,𝔽23)
maximal quotient ofSp(2,𝔽23)

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:

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