Finite Group Databasebeta

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#72226798

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

Aliases

No aliases for this group.

Subgroups

8169 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

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

Polycyclic presentation:

2^10|a^2=h,d^2=f,e^2=j,g^2=i,h^2=j,i^2=j,c^a=cg,d^a=di,e^b=ej,f^a=fj,g^a=gi,g^c=gij,g^d=gj,h^c=hj,i^a=ij,i^c=ij

Conjugacy classes & character table

178 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.8);;
gap> SetPower(coll, 4, F.6);;
gap> SetPower(coll, 5, F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);