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#72231663

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

Aliases

No aliases for this group.

Subgroups

16389 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 28 points:

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

Polycyclic presentation:

2^10|b^2=h,d^2=e,f^2=j,g^2=j,d^a=df,d^b=dg,d^c=dfj,e^a=ej,e^b=ei,e^c=ej,f^a=fj,f^c=fj,g^b=gi,g^d=gij,h^d=hij

Conjugacy classes & character table

148 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.8);;
gap> SetPower(coll, 4, F.5);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 7, F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.6*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);