Finite Group Databasebeta

← Prev (#13088273) Next (#13088275) →

ΣL(2,𝔽9) #13088274

order1440
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

special semilinearΣL(2,𝔽9)

Splittings

derivedSL(2,𝔽9) ⋊ C2

Subgroups

subgroupG/H
center, Frattini, Fitting, socle, hypercenterC2S6
commutator, cosocle, hypocenterSL(2,𝔽9)C2
LCSG ▷ SL(2,𝔽9)
UCSC1 ◁ C2

65 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 80
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 2 generators on 80 points:

(1,2,8,28,15,5,10,29,13,3)(4,16,43,51,48,18,44,53,19,17)(6,23,9,32,40,21,46,33,41,14)(7,25,20,55,42,22,56,52,61,26)(11,36,64,59,24,34,66,31,65,37)(12,38,57,47,68,35,30,27,62,39)(45,67,80,79,60,58,71,78,77,70)(49,74,69,73,76,72,75,54,50,63);(1,4)(2,9)(3,14)(5,18)(6,24)(7,27)(10,33)(11,23)(12,16)(13,28)(15,40)(17,47)(19,54)(20,52)(21,37)(22,57)(25,38)(30,56)(31,49)(32,61)(34,46)(35,44)(36,58)(39,70)(41,55)(43,50)(45,66)(48,62)(51,69)(53,73)(59,77)(60,68)(64,72)(65,79)(67,71)(74,75)

Conjugacy classes & character table

17 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofSp(4,𝔽3), #72224449, #72227518
maximal normal subgroup of#72224449

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4591);