Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C49⋊C9)⋊Dic17 |
| unambiguous semidirect product | Dic833⋊C9 |
| derived, Hall | C17×C49 ⋊ C4×C9 |
| Hall | C17×C49⋊C9 ⋊ C4 |
| Hall | Dic833 ⋊ C9 |
| Hall | C49⋊C9 ⋊ Dic17 |
| Sylow | C49 ⋊ C9×Dic17 |
| Sylow | C17 ⋊ Dic49⋊C9 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 29988 |
Polycyclic presentation:
2,3,7,17,2,3,7|a^2=e,b^3=f,c^7=g^6,c^a=c^6g,d^a=d^16,g^a=g^6,c^b=c^2g^3,g^b=g^2996 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 4);