Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C19×C49 ⋊ C2×C9 |
| Hall | #22552693 ⋊ C2 |
| Hall | C19×D49 ⋊ C9 |
| Hall | D49 ⋊ #4294 |
| Sylow | C49 ⋊ C2×#4294 |
| 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,f^a=f^6,c^b=c^4f^5,d^b=d^7,f^b=f^4510 conjugacy classes — view the full character table.
| maximal subgroup of | #30660480⋊C2, C2×#30660484 |
| maximal normal subgroup of | #30660480⋊C2, C2×#30660484 |
| maximal quotient of | #45691213, C2×#30660484 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 11);