Finite Group DatabasebetaFinite Group Databasebeta| order | 18620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×C19⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C19⋊(AGL(1,𝔽5)×C49) |
| Fitting, Hall | C5×C19×C49 ⋊ C4 |
| derived, Hall | C5×C19 ⋊ C4×C49 |
| Hall | C19×C49 ⋊ AGL(1,𝔽5) |
| Hall | C5×C49 ⋊ Dic19 |
| Sylow | C19 ⋊ AGL(1,𝔽5)×C49 |
| Sylow | C5 ⋊ C49×Dic19 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4655 |
2009 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18620, 12);