Finite Group Databasebeta

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#72313740

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

Aliases

No aliases for this group.

Subgroups

3473 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Polycyclic presentation:

2^10|a^2=f,b^2=h,c^2=f,d^2=fgi,e^2=fh,g^2=i,i^2=j,c^b=ch,d^a=dij,d^b=dh,d^c=dg,e^a=eh,e^b=eh,e^d=ei,f^d=fj,g^a=gj,g^c=gi,g^d=gj,g^e=gj,i^c=ij

Conjugacy classes & character table

109 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.8);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.6*F.7*F.9);;
gap> SetPower(coll, 5, F.6*F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.9*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 7, 5, F.7*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);