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#72319665

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

Aliases

No aliases for this group.

Subgroups

4226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 64 points:

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

Polycyclic presentation:

2^11|b^2=ef,c^2=ghj,d^2=hj,i^2=k,b^a=be,c^a=cg,c^b=cf,d^b=defhij,d^c=dk,e^b=eh,e^c=ei,e^d=ehjk,f^a=fh,f^b=fh,f^c=fhi,f^d=fhjk,g^b=ghi,g^e=gjk,g^f=gj,h^c=hk,i^a=ij,i^c=ij,i^e=ik,i^f=ik,i^g=ik,j^b=jk,j^c=jk

Conjugacy classes & character table

68 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", "k");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 2, F.5*F.6);;
gap> SetPower(coll, 3, F.7*F.8*F.10);;
gap> SetPower(coll, 4, F.8*F.10);;
gap> SetPower(coll, 9, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.5*F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.11);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.8*F.10*F.11);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.8*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.8*F.10*F.11);;
gap> SetConjugate(coll, 7, 2, F.7*F.8*F.9);;
gap> SetConjugate(coll, 7, 5, F.7*F.10*F.11);;
gap> SetConjugate(coll, 7, 6, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.11);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> SetConjugate(coll, 9, 5, F.9*F.11);;
gap> SetConjugate(coll, 9, 6, F.9*F.11);;
gap> SetConjugate(coll, 9, 7, F.9*F.11);;
gap> SetConjugate(coll, 10, 2, F.10*F.11);;
gap> SetConjugate(coll, 10, 3, F.10*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);