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#72236732

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

Aliases

No aliases for this group.

Subgroups

4260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=e,d^2=ei,b^a=bj,c^a=ch,c^b=cg,d^b=df,e^b=eh,f^c=fi,f^d=fhj,g^c=gh,g^d=gij,g^f=gj,i^b=ij

Conjugacy classes & character table

88 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, 3, F.5);;
gap> SetPower(coll, 4, F.5*F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.8*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.8);;
gap> SetConjugate(coll, 7, 4, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 6, F.7*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);