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#72250345

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

Aliases

No aliases for this group.

Subgroups

1856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=h,c^2=ghi,d^2=eghj,e^2=i,i^2=j,c^a=cf,c^b=cfg,d^b=de,d^c=deghij,e^b=ei,e^c=ei,g^c=gj,g^d=gj,h^d=hj,i^b=ij,i^c=ij

Conjugacy classes & character table

100 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.8);;
gap> SetPower(coll, 3, F.7*F.8*F.9);;
gap> SetPower(coll, 4, F.5*F.7*F.8*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);