Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×#4294⋊C2 |
| unambiguous semidirect product | #4294⋊(C2×C49) |
| derived, Sylow | C19 ⋊ C2×C9×C49 |
| Hall | C49×#4294 ⋊ C2 |
| Hall | D19×C49 ⋊ C9 |
| Hall | C19×C49 ⋊ C2×C9 |
| Hall | #4294 ⋊ C2×C49 |
| Hall | D19 ⋊ C9×C49 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8379 |
1323 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D49×#4294⋊C2, C2×C49×#4294⋊C2 |
| maximal normal subgroup of | D49×#4294⋊C2, C2×C49×#4294⋊C2 |
| maximal quotient of | C49×#4294⋊C4, C2×C49×#4294⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 2);