Finite Group DatabasebetaFinite Group Databasebeta| order | 21420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C9×C17 · Schur multiplier (H2) = C1 |
| direct product | C7×C9×C17×AGL(1,𝔽5) |
| Fitting, Hall | C5×C7×C9×C17 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C7×C9×C17 |
| Hall | C5×C9×C17 ⋊ C4×C7 |
| Hall | C5×C7×C17 ⋊ C4×C9 |
| Hall | C5×C7×C9 ⋊ C4×C17 |
| Hall | C5×C17 ⋊ C4×C7×C9 |
| Hall | C5×C9 ⋊ C4×C7×C17 |
| Hall | C5×C7 ⋊ C4×C9×C17 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5355 |
5355 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21420, 55);