Finite Group DatabasebetaFinite Group Databasebeta| order | 26820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C149 · Schur multiplier (H2) = C1 |
| direct product | C149×C9⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C9⋊(AGL(1,𝔽5)×C149) |
| Fitting, Hall | C5×C9×C149 ⋊ C4 |
| derived, Hall | C5×C9 ⋊ C4×C149 |
| Hall | C9×C149 ⋊ AGL(1,𝔽5) |
| Hall | C5×C149 ⋊ Dic9 |
| Sylow | C9 ⋊ AGL(1,𝔽5)×C149 |
| Sylow | C5 ⋊ Dic9×C149 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6705 |
3129 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26820, 19);