Finite Group Databasebeta

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#72259587

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

4290 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 24 points:

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

Polycyclic presentation:

2^3,3^7|e^3=i,f^3=j,e^a=e^2i^2,e^c=e^2i^2,e^d=ei^2,f^a=e^2f,f^c=f^2j^2,f^d=fj^2,g^a=g^2,g^b=g^2,h^a=g^2h,h^b=h^2,i^a=i^2,i^c=i^2,j^a=i^2j,j^c=j^2

Conjugacy classes & character table

174 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, 3, 3, 3, 3, 3, 3, 3]);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 6, F.10);;
gap> SetConjugate(coll, 5, 1, F.5^2*F.9^2);;
gap> SetConjugate(coll, 5, 3, F.5^2*F.9^2);;
gap> SetConjugate(coll, 5, 4, F.5*F.9^2);;
gap> SetConjugate(coll, 6, 1, F.5^2*F.6);;
gap> SetConjugate(coll, 6, 3, F.6^2*F.10^2);;
gap> SetConjugate(coll, 6, 4, F.6*F.10^2);;
gap> SetConjugate(coll, 7, 1, F.7^2);;
gap> SetConjugate(coll, 7, 2, F.7^2);;
gap> SetConjugate(coll, 8, 1, F.7^2*F.8);;
gap> SetConjugate(coll, 8, 2, F.8^2);;
gap> SetConjugate(coll, 9, 1, F.9^2);;
gap> SetConjugate(coll, 9, 3, F.9^2);;
gap> SetConjugate(coll, 10, 1, F.9^2*F.10);;
gap> SetConjugate(coll, 10, 3, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);