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#72284561

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

Aliases

No aliases for this group.

Subgroups

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 64 points:

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

Polycyclic presentation:

2^10|a^2=f,c^2=f,d^2=h,b^a=bh,c^a=cf,c^b=cg,d^a=dg,d^c=dfghij,e^a=ei,e^b=eij,e^d=ej,f^b=fj,f^d=fi,g^a=gi,g^c=gj,g^d=gj,h^a=hj,h^c=hij

Conjugacy classes & character table

67 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, 1, F.6);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.8);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.6*F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.9*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.9);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);