Finite Group DatabasebetaFinite Group Databasebeta| order | 31140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C173 · Schur multiplier (H2) = C1 |
| direct product | C173×C9⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C9⋊(AGL(1,𝔽5)×C173) |
| Fitting, Hall | C5×C9×C173 ⋊ C4 |
| derived, Hall | C5×C9 ⋊ C4×C173 |
| Hall | C9×C173 ⋊ AGL(1,𝔽5) |
| Hall | C5×C173 ⋊ Dic9 |
| Sylow | C9 ⋊ AGL(1,𝔽5)×C173 |
| Sylow | C5 ⋊ Dic9×C173 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7785 |
3633 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31140, 19);