Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#90015 |
| Sylow | C7 ⋊ C22×#458 |
5294 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 5294 conjugacy classes of subgroups — too many to draw. Only its 827 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
268 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1036285);