Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | S4×SD32 |
| Fitting | C22×SD32 ⋊ D3 |
401 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 401 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
55 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#509, S4×#508 |
| maximal normal subgroup of | S4×#509, S4×#508 |
| maximal quotient of | S4×#357, S4×#367 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1088587);