Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C8×#6437 |
| Fitting | C42×C7×C8 ⋊ C2 |
| Sylow | C7 ⋊ C8×#127 |
1350 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 395 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 177949);