Finite Group Databasebeta

?

← Prev (#72329917) Next (#72329919) →

#72329918

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

Aliases

No aliases for this group.

Subgroups

At least 7029 conjugacy classes of subgroups; only the 1095 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 32 points:

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

Polycyclic presentation:

2^10|a^2=f,b^2=fgh,c^2=hij,d^2=gh,b^a=bg,c^a=ci,c^b=cfgh,d^a=dfgh,d^c=di,e^a=eghij,e^b=egj,e^c=ehi,e^d=eghij

Conjugacy classes & character table

142 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.6);;
gap> SetPower(coll, 2, F.6*F.7*F.8);;
gap> SetPower(coll, 3, F.8*F.9*F.10);;
gap> SetPower(coll, 4, F.7*F.8);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.9);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.7*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.6*F.7*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.7*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.8*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.7*F.8*F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);