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#72335341

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

Aliases

No aliases for this group.

Subgroups

57673 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

(1,2,4,3)(5,6,8,7)(9,10,11,12)(14,17)(18,19);(1,2,4,3)(5,6,8,7)(13,14)(15,18)(16,17)(19,20);(2,3)(6,7)(14,17)(18,19);(2,3)(13,15)(14,18)(16,20)(17,19);(6,7)(13,15)(14,18)(16,20)(17,19);(1,3,4,2)(5,7,8,6)(13,14)(15,19)(16,17)(18,20)

Polycyclic presentation:

2^10|a^2=g,b^2=gj,f^2=gj,b^a=bgi,c^a=cgj,c^b=cij,d^a=dgh,d^b=dgh,e^a=ehj,e^b=ehj,f^a=fgi,f^c=fij,f^d=fhi,f^e=fghij

Conjugacy classes & character table

244 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.7*F.10);;
gap> SetPower(coll, 6, F.7*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7*F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.9*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.8*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.7*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.8*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.7*F.8*F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);