Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | A4×#444 |
| unambiguous semidirect product | (C22×#444)⋊C3 |
| Fitting, Sylow | C22×#444 ⋊ C3 |
625 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 625 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | A4×AGL(1,ℤ/16), #72241438, S4×#444, … |
| maximal normal subgroup of | A4×AGL(1,ℤ/16), #72241438, S4×#444 |
| maximal quotient of | A4×#1580 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084652);