Finite Group DatabasebetaFinite Group Databasebeta| order | 9408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | #72215163 ⋊ C3 |
| Hall | #3861 ⋊ C2×#99 |
| Sylow | C72 ⋊ C2×C3×#99 |
1548 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1548 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^3,3,2^3,7^2|a^2=f,b^a=be,e^a=eg,f^b=fg,h^a=h^6,h^c=h^6,h^d=h^2,i^a=h^2i,i^c=i^6,i^d=i^2118 conjugacy classes — view the full character table.
| maximal subgroup of | #72215186 |
| maximal normal subgroup of | #72215186 |
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, 2, 7, 7]);;
gap> SetPower(coll, 1, F.6);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.7);;
gap> SetConjugate(coll, 6, 2, F.6*F.7);;
gap> SetConjugate(coll, 8, 1, F.8^6);;
gap> SetConjugate(coll, 8, 3, F.8^6);;
gap> SetConjugate(coll, 8, 4, F.8^2);;
gap> SetConjugate(coll, 9, 1, F.8^2*F.9);;
gap> SetConjugate(coll, 9, 3, F.9^6);;
gap> SetConjugate(coll, 9, 4, F.9^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);