Finite Group Databasebeta

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#72253777

• supersolvable
• solvable
• monomial
• stem
• ambivalent

Aliases

No aliases for this group.

Splittings

Subgroups

4852 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9,3|b^2=e,e^2=i,b^a=bg,c^a=ci,c^b=cef,d^b=dei,e^c=ei,e^d=ei,f^a=fh,g^c=ghi,g^f=gi,h^b=hi,j^d=j^2

Conjugacy classes & character table

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