Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C32×#7463 ⋊ C2 |
| Sylow | C32 ⋊ #151085 |
924 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2304 |
Polycyclic presentation:
2^9,3^2|a^2=e,b^2=eg,c^2=dfh,d^2=fhi,e^2=g,f^2=hi,h^2=i,c^a=cd,c^b=chi,d^a=df,d^b=di,e^c=ei,f^a=fh,h^a=hi,j^b=j^2,k^b=k^2276 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#151085 |
| maximal normal subgroup of | C3⋊D3×#151085 |
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", "k");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3]);;
gap> SetPower(coll, 1, F.5);;
gap> SetPower(coll, 2, F.5*F.7);;
gap> SetPower(coll, 3, F.4*F.6*F.8);;
gap> SetPower(coll, 4, F.6*F.8*F.9);;
gap> SetPower(coll, 5, F.7);;
gap> SetPower(coll, 6, F.8*F.9);;
gap> SetPower(coll, 8, F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.4);;
gap> SetConjugate(coll, 3, 2, F.3*F.8*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 10, 2, F.10^2);;
gap> SetConjugate(coll, 11, 2, F.11^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);