Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C23 |
| direct product | A4×C22⋊C16 |
| unambiguous semidirect product | (C22×C22⋊C16)⋊C3 |
| Fitting, Sylow | C22×C22⋊C16 ⋊ C3 |
355 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 355 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#2112, A4×A4⋊C16 |
| maximal normal subgroup of | A4×#2112 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084037);