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#72340263

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

Aliases

No aliases for this group.

Subgroups

2744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=g,d^2=gi,e^2=ij,b^a=bi,c^a=cg,c^b=cf,d^a=dgij,d^b=dh,e^a=efghij,e^b=eh,e^c=eh,e^d=efg,f^a=fi,f^c=fi,f^d=fj,f^e=fj,g^b=gi,g^e=gj,h^a=hi,h^c=hj,h^d=hi

Conjugacy classes & character table

64 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, 3, F.7);;
gap> SetPower(coll, 4, F.7*F.9);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.9*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.6*F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.6*F.7);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 5, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);