Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×C49⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C49⋊(AGL(1,𝔽5)×C29) |
| Fitting, Hall | C5×C29×C49 ⋊ C4 |
| derived, Hall | C5×C49 ⋊ C4×C29 |
| Hall | C29×C49 ⋊ AGL(1,𝔽5) |
| Hall | C5×C29 ⋊ Dic49 |
| Sylow | C49 ⋊ AGL(1,𝔽5)×C29 |
| Sylow | C5 ⋊ C29×Dic49 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7105 |
2929 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 32);