Finite Group Databasebeta

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#72226114

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

5236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 23 points:

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

Polycyclic presentation:

2^9,3|b^2=f,c^2=fg,d^2=g,e^2=h,h^2=i,c^a=ch,c^b=cg,d^a=dhi,d^b=dg,e^a=ehi,e^b=eh,e^c=ei,g^a=gi,h^a=hi,h^b=hi,j^b=j^2

Conjugacy classes & character table

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