Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×D3×SD64 |
| Fitting | C2×C3×SD64 ⋊ C2 |
| Sylow | C3 ⋊ C22×SD64 |
502 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2263 |
| maximal normal subgroup of | C2×D3×#2263 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 327685);