Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | D3×#1410 |
| Fitting | C3×#1410 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1410 |
450 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
51 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 89891);