Finite Group Databasebeta

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#72252374

• supersolvable
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

2161 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 22 points:

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

Polycyclic presentation:

2^8,3^2|a^2=gh,c^2=de,f^2=h,c^a=cf,c^b=cd,d^a=dg,e^a=egh,f^b=fgh,f^d=fh,f^e=fh,g^c=gh,i^a=i^2,i^c=i^2,j^a=i^2j,j^c=j^2

Conjugacy classes & character table

126 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, 3, 3]);;
gap> SetPower(coll, 1, F.7*F.8);;
gap> SetPower(coll, 3, F.4*F.5);;
gap> SetPower(coll, 6, F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.4);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.7*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.7*F.8);;
gap> SetConjugate(coll, 6, 4, F.6*F.8);;
gap> SetConjugate(coll, 6, 5, F.6*F.8);;
gap> SetConjugate(coll, 7, 3, F.7*F.8);;
gap> SetConjugate(coll, 9, 1, F.9^2);;
gap> SetConjugate(coll, 9, 3, F.9^2);;
gap> SetConjugate(coll, 10, 1, F.9^2*F.10);;
gap> SetConjugate(coll, 10, 3, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);