Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C32 · Schur multiplier (H2) = C2 |
| direct product | C3×C4⋊#3928 |
| unambiguous semidirect product | C4⋊(C3×#3928) |
| Hall | C3×C5 ⋊ C4⋊C32 |
| Sylow | C5 ⋊ C3×C4⋊C32 |
124 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1920 |
336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5387);