Finite Group Databasebeta

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#72253318

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

4830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

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

Polycyclic presentation:

2^9,3|b^2=g,e^2=i,g^2=i,h^2=i,b^a=be,c^a=cf,c^b=cghi,d^a=dfh,d^b=deh,e^a=ei,e^b=ei,e^d=ei,f^b=fi,g^d=gi,h^a=hi,h^d=hi,j^d=j^2

Conjugacy classes & character table

114 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.7);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.7*F.8*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.6*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.5*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.9);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.9);;
gap> SetConjugate(coll, 10, 4, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);