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#72239293

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

Aliases

No aliases for this group.

Subgroups

4307 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=e,b^2=egij,c^2=f,d^2=j,e^2=j,g^2=ij,b^a=bg,c^a=cgh,c^b=cgi,e^b=ei,f^a=fi,f^b=fi,g^a=gj,g^b=gi,g^c=gj,h^a=hi,h^b=hi

Conjugacy classes & character table

148 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.5);;
gap> SetPower(coll, 2, F.5*F.7*F.9*F.10);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.10);;
gap> SetPower(coll, 5, F.10);;
gap> SetPower(coll, 7, F.9*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.7*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);