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#72309580

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

Aliases

No aliases for this group.

Subgroups

4923 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

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

Polycyclic presentation:

2^10|a^2=h,b^2=f,c^2=j,d^2=fj,g^2=i,h^2=j,b^a=bhj,c^a=cg,d^a=dj,d^b=dj,d^c=dgi,e^a=ei,e^b=ej,e^d=ei,g^a=gi,g^c=gi,g^d=gi,h^b=hj

Conjugacy classes & character table

130 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.8);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 3, F.10);;
gap> SetPower(coll, 4, F.6*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.7*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);