Finite Group Databasebeta

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#72319236

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

Aliases

No aliases for this group.

Subgroups

2849 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=f,c^2=fgij,f^2=h,g^2=i,h^2=j,i^2=j,b^a=bhi,c^b=ci,d^c=dj,e^c=ehi,f^c=fj,g^b=gj,g^c=gj

Conjugacy classes & character table

208 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.6*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> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8*F.9);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.8*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);