Finite Group Databasebeta

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#72226560

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

1230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^7,5^2|a^2=f,f^2=g,b^a=bfg,c^a=cg,d^a=de,d^b=dfg,e^a=eg,e^b=eg,f^b=fg,f^d=fg,h^a=h^4,h^b=h^4,i^a=h^3i,i^b=i^4

Conjugacy classes & character table

197 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");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 5, 5]);;
gap> SetPower(coll, 1, F.6);;
gap> SetPower(coll, 6, F.7);;
gap> SetConjugate(coll, 2, 1, F.2*F.6*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.7);;
gap> SetConjugate(coll, 5, 2, F.5*F.7);;
gap> SetConjugate(coll, 6, 2, F.6*F.7);;
gap> SetConjugate(coll, 6, 4, F.6*F.7);;
gap> SetConjugate(coll, 8, 1, F.8^4);;
gap> SetConjugate(coll, 8, 2, F.8^4);;
gap> SetConjugate(coll, 9, 1, F.8^3*F.9);;
gap> SetConjugate(coll, 9, 2, F.9^4);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);