Finite Group Databasebeta

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#72269039

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

2685 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 25 points:

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

Polycyclic presentation:

2^8,3^2|a^2=f,f^2=h,i^3=j,b^a=bg,c^a=cfh,c^b=ce,d^a=dh,d^b=de,e^a=eh,f^b=fh,f^c=fh,g^a=gh,g^d=gh,i^b=i^2j^2,i^d=i^2j^2,j^b=j^2,j^d=j^2

Conjugacy classes & character table

132 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, 3, 3]);;
gap> SetPower(coll, 1, F.6);;
gap> SetPower(coll, 6, F.8);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.6*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.8);;
gap> SetConjugate(coll, 7, 4, F.7*F.8);;
gap> SetConjugate(coll, 9, 2, F.9^2*F.10^2);;
gap> SetConjugate(coll, 9, 4, F.9^2*F.10^2);;
gap> SetConjugate(coll, 10, 2, F.10^2);;
gap> SetConjugate(coll, 10, 4, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);