Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | S4×#117 |
| Fitting | C22×#117 ⋊ D3 |
1823 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 1823 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#421, #72341494, S4×#525, … |
| maximal normal subgroup of | S4×#421, S4×#525, S4×#418 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1088683);