Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#19153589 |
| Fitting, Hall | C3×C5×C289 ⋊ C4 |
| derived, Hall | C5×C289 ⋊ C3×C4 |
| Hall | C3×C289 ⋊ AGL(1,𝔽5) |
| Sylow | C289 ⋊ C3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ Dic289 |
| Sylow | C5 ⋊ C3×Dic289 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4335 |
1743 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 14);