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#72262401

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

Aliases

No aliases for this group.

Subgroups

3865 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 32 points:

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

Polycyclic presentation:

2^10|a^2=f,b^2=gh,g^2=j,b^a=bg,c^a=ce,c^b=cefj,d^a=dfhi,d^b=dj,d^c=dfi,e^b=ei,f^b=fj,g^c=gi,g^e=gj,h^a=hj,h^c=hj,i^a=ij,i^b=ij

Conjugacy classes & character table

70 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.6);;
gap> SetPower(coll, 2, F.7*F.8);;
gap> SetPower(coll, 7, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.5*F.6*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.6*F.8*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.6*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 7, 5, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);