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#72320384

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

Aliases

No aliases for this group.

Subgroups

5377 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=i,b^2=f,e^2=hj,i^2=j,b^a=bij,c^b=ch,d^a=di,d^c=dh,e^a=ehij,e^b=eh,e^c=efg,e^d=egj,i^b=ij,i^d=ij,i^e=ij

Conjugacy classes & character table

112 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.9);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 5, F.8*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.6*F.7);;
gap> SetConjugate(coll, 5, 4, F.5*F.7*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 4, F.9*F.10);;
gap> SetConjugate(coll, 9, 5, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);