Finite Group Databasebeta

?

← Prev (#72335381) Next (#72335383) →

#72335382

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

Aliases

No aliases for this group.

Subgroups

At least 6209 conjugacy classes of subgroups; only the 5589 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

Polycyclic presentation:

2^10|d^2=h,e^2=gh,f^2=gij,b^a=bg,c^b=ci,d^a=dj,d^c=dg,e^a=ej,e^c=eg,e^d=eg,f^d=fgij

Conjugacy classes & character table

178 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, 4, F.8);;
gap> SetPower(coll, 5, F.7*F.8);;
gap> SetPower(coll, 6, F.7*F.9*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.7);;
gap> SetConjugate(coll, 5, 4, F.5*F.7);;
gap> SetConjugate(coll, 6, 4, F.6*F.7*F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);