Finite Group Databasebeta

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#72331702

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

Aliases

No aliases for this group.

Subgroups

At least 10210 conjugacy classes of subgroups; only the 3617 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

(1,2)(3,4)(6,8)(9,10)(11,15)(12,14)(13,16)(19,20)(21,24);(1,2)(3,4)(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18,22,23)(19,24,20,21);(1,2)(3,4)(9,10,12,14)(11,15,16,13)(17,19,22,20)(18,21,23,24);(2,4)(11,16)(13,15);(1,2)(3,4)(9,10)(11,13)(12,14)(15,16)(17,20,22,19)(18,21,23,24);(1,2)(3,4)(9,11)(10,13)(12,16)(14,15)(17,21)(18,19)(20,23)(22,24)

Polycyclic presentation:

2^10|b^2=gj,c^2=i,e^2=gj,b^a=bg,c^a=ci,c^b=ci,d^a=dh,d^b=dh,d^c=dh,e^a=egj,e^c=egij,e^d=eh,f^a=fi,f^c=fi,f^d=fghij

Conjugacy classes & character table

136 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, 2, F.7*F.10);;
gap> SetPower(coll, 3, F.9);;
gap> SetPower(coll, 5, F.7*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.9);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.7*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.7*F.9*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.7*F.8*F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);