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#72318984

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

Aliases

No aliases for this group.

Subgroups

995 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=f,c^2=e,d^2=ehj,e^2=h,f^2=i,i^2=j,b^a=bh,c^a=cgj,c^b=cfhij,d^a=dg,d^b=dhij,d^c=dj,e^b=ej,f^c=fi,f^d=fj,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, 1, F.7);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 4, F.5*F.8*F.10);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 6, 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*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);