Finite Group Databasebeta

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#72323025

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Subgroups

2213 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 48 points:

(17,18,20,26,21,27,31,40,22,25,32,23,33,35,44,36)(19,24,29,38,30,39,43,47,28,37,41,34,42,45,48,46);(1,2,4,8,5,7,12,15)(3,9,11,16,10,6,13,14)(18,23,25,26)(20,31)(21,33)(24,34,37,38)(27,40,35,36)(29,43)(30,42)(32,44)(39,47,45,46)(41,48);(1,3)(2,6)(4,11)(5,10)(7,9)(8,14)(12,13)(15,16);(2,7)(3,10)(8,15)(11,13)(17,19)(18,24)(20,29)(21,30)(22,28)(23,34)(25,37)(26,38)(27,39)(31,43)(32,41)(33,42)(35,45)(36,46)(40,47)(44,48);(19,28)(24,37)(29,41)(30,42)(34,38)(39,45)(43,48)(46,47)

Polycyclic presentation:

2^10|a^2=g,b^2=f,f^2=h,g^2=i,i^2=j,b^a=bgi,c^b=ch,d^b=dh,d^c=dh,e^d=ej,f^a=fj,g^b=gi,i^b=ij

Conjugacy classes & character table

148 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, 2]);;
gap> SetPower(coll, 1, F.7);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 6, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7*F.9);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);