Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C8 |
| direct product | C2×#68059 |
| Fitting | C2×C3×C82 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1708 |
866 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 267 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 157222);