Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | A4×#465 |
| unambiguous semidirect product | (C22×#465)⋊C3 |
| Fitting, Sylow | C22×#465 ⋊ C3 |
765 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 765 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#3050, A4×#5401 |
| maximal normal subgroup of | A4×#3050 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084747);