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#72256887

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

Aliases

No aliases for this group.

Subgroups

3818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=h,b^2=f,c^2=fgi,d^2=fj,g^2=i,i^2=j,c^a=ce,c^b=cg,d^a=dfhj,d^c=de,e^d=ej,f^c=fj,g^b=gi,g^c=gj,i^b=ij

Conjugacy classes & character table

112 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.8);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 3, F.6*F.7*F.9);;
gap> SetPower(coll, 4, F.6*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.6*F.8*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
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);