Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C49 · Schur multiplier (H2) = C1 |
| direct product | C2×C49×#4294 |
| derived, Sylow | C19 ⋊ C2×C9×C49 |
| Hall | C2×C19×C49 ⋊ C9 |
| Hall | C19×C49 ⋊ C2×C9 |
| Hall | C2×C19 ⋊ C9×C49 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16758 |
2646 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C49×#4294⋊C4, #4294×Dic49, #4294⋊Dic49, … |
| maximal normal subgroup of | C49×#4294⋊C4, #4294×Dic49, #4294⋊Dic49, … |
| maximal quotient of | C4×C49×#4294, C22×C49×#4294 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 14);