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#72310964

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

Aliases

No aliases for this group.

Subgroups

2903 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=f,d^2=ghi,b^a=bij,c^a=ch,c^b=ci,d^a=dfg,d^b=dfhij,d^c=dgi,e^a=eh,e^b=ehi,e^c=egh,e^d=ei,f^a=fi,f^d=fij,f^e=fj,g^a=gi,g^b=gi,g^c=gij,g^d=gj,h^c=hi,h^d=hj

Conjugacy classes & character table

58 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.6);;
gap> SetPower(coll, 4, F.7*F.8*F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.9*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.6*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.7*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.7*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);