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#72287017

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

Aliases

No aliases for this group.

Subgroups

2006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,d^2=e,e^2=h,f^2=ij,g^2=i,i^2=j,b^a=bh,c^a=cg,d^a=df,d^b=dh,e^a=ej,f^c=fi,f^d=fij,g^c=gij,g^d=gi,i^c=ij,i^d=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.7);;
gap> SetPower(coll, 4, F.5);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 6, F.9*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.9*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.9);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> SetConjugate(coll, 9, 4, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);