Finite Group Databasebeta

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#72226431

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

5316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Polycyclic presentation:

2^8,5^2|a^2=f,b^2=e,f^2=h,b^a=bfg,c^b=ce,e^a=eh,g^a=gh,g^c=gh,i^a=i^4,i^d=i^4,j^a=i^3j,j^d=j^4

Conjugacy classes & character table

304 conjugacy classes — view the full character table.

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