Finite Group Databasebeta

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#72284219

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

Aliases

No aliases for this group.

Subgroups

3491 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 32 points:

(2,6)(3,9)(8,14)(15,16)(17,18)(19,23)(20,24)(21,22)(25,31)(26,27)(28,32)(29,30);(4,12)(11,13)(17,19)(18,23)(20,28)(21,26)(22,27)(24,32)(25,29)(30,31);(1,2)(3,10,9,7)(4,8)(5,6)(11,16,13,15)(12,14)(17,20)(18,24)(19,25,27,28)(21,30)(22,29)(23,31,26,32);(1,3,5,9)(2,7,6,10)(4,13)(8,16)(11,12)(14,15)(17,21,22,18)(19,26,27,23)(20,24)(25,31)(28,32)(29,30);(1,4)(2,8)(3,11)(5,12)(6,14)(7,15)(9,13)(10,16)(19,27)(25,28)

Polycyclic presentation:

2^10|c^2=f,d^2=hij,c^a=ci,c^b=ch,d^a=dhij,d^c=dg,e^a=ef,e^b=egij,e^d=ef,f^b=fj,f^d=fi,g^a=gj,g^c=gi,g^d=gj,h^c=hj,h^e=hi

Conjugacy classes & character table

61 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.8*F.9*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.9);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.6);;
gap> SetConjugate(coll, 5, 2, F.5*F.7*F.9*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.6);;
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.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 8, 5, F.8*F.9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);