Finite Group Databasebeta

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#72227360

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

6036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

(1,4,5,17,6,18,20,28)(2,9,10,25,8,15,23,31)(3,12,14,30,13,29,19,16)(7,22,11,27,21,32,26,24)(33,34,35)(36,37,38);(34,35)(37,38);(2,8)(7,21)(9,15)(10,23)(11,26)(22,32)(24,27)(25,31);(1,3)(2,7)(4,16)(5,19)(6,13)(8,21)(9,24)(10,26)(11,23)(12,28)(14,20)(15,27)(17,29)(18,30)(22,31)(25,32);(1,2)(3,11,13,26)(4,15)(5,10)(6,8)(7,14,21,19)(9,18)(12,24,29,27)(16,32,30,22)(17,31)(20,23)(25,28)(37,38)

Polycyclic presentation:

2^8,3^2|a^2=f,e^2=g,g^2=h,b^a=bg,c^a=ch,e^a=eh,e^b=egh,f^b=fh,g^b=gh,i^a=i^2,i^d=i^2,j^a=i^2j,j^d=j^2

Conjugacy classes & character table

204 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, 3, 3]);;
gap> SetPower(coll, 1, F.6);;
gap> SetPower(coll, 5, F.7);;
gap> SetPower(coll, 7, F.8);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.7*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
gap> SetConjugate(coll, 7, 2, F.7*F.8);;
gap> SetConjugate(coll, 9, 1, F.9^2);;
gap> SetConjugate(coll, 9, 4, F.9^2);;
gap> SetConjugate(coll, 10, 1, F.9^2*F.10);;
gap> SetConjugate(coll, 10, 4, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);