Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#14558786 |
| derived | C7×C19 ⋊ C2×C7×C9 |
| Hall | C7×#11924776 ⋊ C2 |
| Hall | C7×D133 ⋊ C9 |
| Hall | C72×C19 ⋊ C2×C9 |
| Sylow | C72 ⋊ #4294⋊C2 |
| Sylow | C19 ⋊ C7×D7⋊C9 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2394 |
588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#14558780⋊C2, D7×#14558786, #14558786⋊D7, … |
| maximal normal subgroup of | C7×#14558780⋊C2, D7×#14558786, #14558786⋊D7, … |
| maximal quotient of | C7×#18012096, C2×C7×#14558786 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 88);