Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C16 · Schur multiplier (H2) = C1 |
| direct product | C5×C16×SL(2,𝔽3) |
| unambiguous semidirect product | (Q8×C16)⋊(C3×C5) |
| unambiguous semidirect product | (C5×Q8×C16)⋊C3 |
| Fitting, Hall | C5×Q8×C16 ⋊ C3 |
| derived | Q8 ⋊ C3×C5×C16 |
| Sylow | Q8×C16 ⋊ C3×C5 |
108 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 48 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, 236397);