Finite Group Databasebeta

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#72340492

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

Aliases

No aliases for this group.

Subgroups

2728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,b^2=fgj,c^2=ij,b^a=bg,c^a=cgh,d^a=dh,d^b=dj,d^c=dfg,e^a=eh,e^b=ehij,e^c=eghij,f^b=fi,f^c=fij,f^d=fj,f^e=fj,g^a=gi,g^b=gi,g^c=gij,g^d=gj,h^a=hj,h^b=hj,h^c=hij

Conjugacy classes & character table

64 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, 1, F.6);;
gap> SetPower(coll, 2, F.6*F.7*F.10);;
gap> SetPower(coll, 3, F.9*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.6*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);