Finite Group Databasebeta

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#72321764

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Subgroups

2300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 48 points:

(19,30)(20,34)(21,33)(22,23)(26,39)(27,40)(28,29)(31,41)(32,37)(35,46)(36,45)(38,42)(43,47)(44,48);(1,2)(3,7)(4,8)(5,6)(9,14)(10,12)(11,13)(15,16)(17,18,24,25)(19,31,21,26)(20,27,37,38)(22,28,23,29)(30,41,33,39)(32,42,34,40)(35,43,36,44)(45,48,46,47);(2,6)(7,12)(8,13)(14,16)(18,25)(26,31)(27,38)(28,29)(39,41)(40,42)(43,44)(47,48);(1,3,4,9,5,10,11,15)(2,7,8,14,6,12,13,16)(17,19,22,33,24,21,23,30)(18,26,28,41,25,31,29,39)(20,34,35,45,37,32,36,46)(27,42,43,47,38,40,44,48);(17,20,33,46,23,36,19,32,24,37,30,45,22,35,21,34)(18,27,39,47,29,44,31,42,25,38,41,48,28,43,26,40)

Polycyclic presentation:

2^10|b^2=j,d^2=g,e^2=fh,f^2=hj,g^2=i,h^2=j,c^b=ci,d^a=dh,d^b=dj,e^a=ef,e^d=ej,f^a=fh,g^a=gj,h^a=hj

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f", "g", "h", "i", "j");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 2, F.10);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.6*F.8);;
gap> SetPower(coll, 6, F.8*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.6);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);