Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C24×C3×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ #120 |
1903 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 1903 conjugacy classes of subgroups — too many to draw. Only its 262 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^3,3,2^2,3^3|g^3=i,b^a=be,c^a=cf,g^a=g^2i^2,g^d=gi^2,h^a=h^2,i^a=i^2282 conjugacy classes — view the full character table.
| maximal subgroup of | #72220043, #120×C3⋊AGL(1,ℤ/9), #72220141 |
| maximal normal subgroup of | #120×C3⋊AGL(1,ℤ/9), #72220141 |
| maximal quotient of | #72220043 |
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");;
gap> coll := SingleCollector(F, [2, 2, 2, 3, 2, 2, 3, 3, 3]);;
gap> SetPower(coll, 7, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 7, 1, F.7^2*F.9^2);;
gap> SetConjugate(coll, 7, 4, F.7*F.9^2);;
gap> SetConjugate(coll, 8, 1, F.8^2);;
gap> SetConjugate(coll, 9, 1, F.9^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);