Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42×C5 · Schur multiplier (H2) = C4 |
| direct product | C4×C5×#131⋊C3 |
| unambiguous semidirect product | (C4×#131)⋊(C3×C5) |
| unambiguous semidirect product | (C4×C5×#131)⋊C3 |
| Fitting, Hall | C4×C5×#131 ⋊ C3 |
| Sylow | C4×#131 ⋊ C3×C5 |
314 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
560 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236647);