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PSL(3,𝔽4) #72209755

order20160
isoclinismisoclinic class of PSL(3,𝔽4)
automorphism?
homologyAbelianization (H1) = C1 · Schur multiplier (H2) = C3×C42

Aliases

projective special linearPSL(3,𝔽4)

Subgroups

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

95 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

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

Conjugacy classes & character table

C1C2C3C4C5C6C7C8C9C10
size131512601260126022402880288040324032
order1244437755
χ11111111111
χ22040002-1-100
χ33533-1-1-10000
χ4353-13-1-10000
χ5353-1-13-10000
χ645-31110−1+i72−1−i7200
χ745-31110−1−i72−1+i7200
χ863-1-1-1-10001+521−52
χ963-1-1-1-10001−521+52
χ10640000111-1-1

Here i is the imaginary unit (i² = −1).

Relationships

maximal subgroup ofPGL(3,𝔽4), PΣL(3,𝔽4)
maximal normal subgroup ofPGL(3,𝔽4), PΣL(3,𝔽4)
maximal quotient ofSL(3,𝔽4), #72227519

GAP

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

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