Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#41×SL(2,𝔽3) |
| Fitting, Hall | C5×Q8×#41 ⋊ C3 |
| Sylow | Q8×#41 ⋊ C3×C5 |
696 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237036);