Finite Group Databasebeta

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#72227390

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

5940 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Polycyclic presentation:

2^8,3^2|b^2=f,c^2=f,d^2=g,e^2=g,g^2=h,d^a=dh,d^b=dg,d^c=dh,e^b=eg,e^c=eh,g^b=gh,i^a=i^2,i^e=i^2,j^a=i^2j,j^e=j^2

Conjugacy classes & character table

192 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, 2, F.6);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.7);;
gap> SetPower(coll, 7, F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.7);;
gap> SetConjugate(coll, 5, 3, F.5*F.8);;
gap> SetConjugate(coll, 7, 2, F.7*F.8);;
gap> SetConjugate(coll, 9, 1, F.9^2);;
gap> SetConjugate(coll, 9, 5, F.9^2);;
gap> SetConjugate(coll, 10, 1, F.9^2*F.10);;
gap> SetConjugate(coll, 10, 5, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);