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#72343015

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

Aliases

No aliases for this group.

Subgroups

2545 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,c^2=h,f^2=h,g^2=i,i^2=j,b^a=bi,c^a=ch,e^a=eg,e^b=eg,e^d=eh,f^e=fj,g^a=gi,g^b=gij,g^e=gij,i^a=ij,i^b=ij,i^e=ij

Conjugacy classes & character table

106 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.8);;
gap> SetPower(coll, 6, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.7);;
gap> SetConjugate(coll, 5, 2, F.5*F.7);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
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*F.10);;
gap> SetConjugate(coll, 7, 5, F.7*F.9*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 5, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);