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#72257229

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

Aliases

No aliases for this group.

Subgroups

3379 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=e,c^2=i,d^2=hj,e^2=j,h^2=j,b^a=bf,c^b=ch,d^a=dg,d^b=dei,d^c=dj,e^a=ei,f^b=fi,f^d=fij,f^e=fj,h^b=hj,i^b=ij

Conjugacy classes & character table

82 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, 2, F.5);;
gap> SetPower(coll, 3, F.9);;
gap> SetPower(coll, 4, F.8*F.10);;
gap> SetPower(coll, 5, F.10);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.5*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);