Finite Group Databasebeta

?

← Prev (#72321993) Next (#72321995) →

#72321994

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

Aliases

No aliases for this group.

Subgroups

2298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=f,c^2=i,e^2=gij,f^2=h,g^2=i,h^2=j,b^a=bg,d^c=dij,e^a=eg,e^b=ei,e^c=ei,f^a=fi,g^a=gi

Conjugacy classes & character table

220 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, 2]);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 3, F.9);;
gap> SetPower(coll, 5, F.7*F.9*F.10);;
gap> SetPower(coll, 6, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.7);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);