Finite Group Databasebeta

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#72271783

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

Polycyclic presentation:

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

Conjugacy classes & character table

123 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, 4, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.7*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, 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, 3, F.7*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.9);;
gap> SetConjugate(coll, 10, 1, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);