Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | S4×#107 |
| Fitting | C22×#107 ⋊ D3 |
605 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 605 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D8×S4, S4×#357, S4×#367 |
| maximal normal subgroup of | C4×D8×S4, S4×#357, S4×#367 |
| maximal quotient of | S4×#368, S4×#367 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087386);