Finite Group DatabasebetaFinite Group Databasebeta| order | 1890 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C9 · Schur multiplier (H2) = C3 |
| direct product | C5×C9×AGL(1,𝔽7) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C2×C5×C9) |
| Fitting | C5×C7×C9 ⋊ C2×C3 |
| derived, Sylow | C7 ⋊ C2×C3×C5×C9 |
| Hall | C5×C9×ΓL(1,𝔽8) ⋊ C2 |
| Hall | C9×ΓL(1,𝔽8) ⋊ C2×C5 |
| Hall | C5×D7 ⋊ C3×C9 |
| Hall | C5×C7 ⋊ C2×C3×C9 |
| Hall | D7 ⋊ C3×C5×C9 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 315 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1890, 13);