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#72265193

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

Aliases

No aliases for this group.

Subgroups

2105 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 36 points:

(1,2,4,3)(6,12,16,17)(8,14)(13,24,28,26)(15,30,31,25)(18,29)(21,22)(27,35,36,34)(32,33);(1,2,4,3)(6,13,16,28)(8,21)(9,11)(12,24,17,26)(14,22)(15,27,31,36)(18,32)(19,23)(25,34,30,35)(29,33);(2,3)(5,6,14,28,11,17,22,26,10,16,8,13,9,12,21,24)(7,15,29,36,19,30,33,35,20,31,18,27,23,25,32,34);(1,3,4,2)(5,7)(6,15)(8,18)(9,23)(10,20)(11,19)(12,25)(13,27)(14,29)(16,31)(17,30)(21,32)(22,33)(24,34)(26,35)(28,36)

Polycyclic presentation:

2^10|a^2=g,b^2=g,c^2=eh,d^2=hj,e^2=i,f^2=j,i^2=j,c^a=cf,c^b=ce,d^a=dghj,d^c=dhj,e^a=ej,e^b=ei,f^b=fj,f^d=fj,g^c=gj,i^b=ij

Conjugacy classes & character table

88 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.7);;
gap> SetPower(coll, 2, F.7);;
gap> SetPower(coll, 3, F.5*F.8);;
gap> SetPower(coll, 4, F.8*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.8*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);