Finite Group Databasebeta

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#72271749

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

2234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 35 points:

(1,2,3)(5,12)(7,20)(8,23)(10,15)(11,28)(13,14)(17,22)(19,32)(24,27)(25,26)(29,30)(33,35);(2,3)(4,7)(5,11)(6,16,18,31)(8,21)(9,20)(10,24,25,33)(12,30)(13,29)(14,28)(15,27,26,35)(17,32,22,19)(23,34);(4,6)(5,10,13,25)(7,19,20,32)(8,22)(9,18)(11,27)(12,26,14,15)(16,21,31,34)(17,23)(24,30)(28,33)(29,35);(4,5,8,14,9,13,23,12)(6,15,17,10,18,26,22,25)(7,11,21,28,20,29,34,30)(16,27,32,24,31,35,19,33)

Polycyclic presentation:

2^9,3|a^2=g,b^2=e,c^2=h,g^2=i,b^a=bgh,c^b=cgh,d^a=dgh,d^b=df,d^c=dhi,e^a=ei,e^c=ei,f^a=fi,g^b=gi,g^d=gi,h^b=hi,j^c=j^2

Conjugacy classes & character table

135 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, 1, F.7);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.7*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.7*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.9);;
gap> SetConjugate(coll, 10, 3, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);