Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C49 · Schur multiplier (H2) = C3 |
| direct product | C32×D19×C49 |
| Fitting, Hall | C32×C19×C49 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C32×C49 |
| Hall | C19×C49 ⋊ C2×C32 |
| Hall | C32×C19 ⋊ C2×C49 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8379 |
4851 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D19×D49, C3×D3×D19×C49, C3×D19×D147, … |
| maximal normal subgroup of | C32×D19×D49, C3×D3×D19×C49, C3×D19×D147, … |
| maximal quotient of | C32×C49×Dic19, C2×C32×D19×C49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 74);