Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C49⋊C9)⋊D19 |
| derived, Hall | C19×C49 ⋊ C2×C9 |
| Hall | C19×C49⋊C9 ⋊ C2 |
| Hall | D931 ⋊ C9 |
| Hall | C49⋊C9 ⋊ D19 |
| Sylow | C49 ⋊ C9×D19 |
| Sylow | C19 ⋊ D49⋊C9 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8379 |
Polycyclic presentation:
2,3,7,19,3,7|b^3=e,c^7=f^6,c^a=c^6f,d^a=d^18,f^a=f^6,c^b=c^2f^3,f^b=f^2555 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D49⋊C9, C2×(C49⋊C9)⋊D19 |
| maximal normal subgroup of | D19×D49⋊C9, C2×(C49⋊C9)⋊D19 |
| maximal quotient of | (C49⋊C9)⋊Dic19, C2×(C49⋊C9)⋊D19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 9);