Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | A4×#447 |
| unambiguous semidirect product | (C22×#447)⋊C3 |
| Fitting, Sylow | C22×#447 ⋊ C3 |
1575 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 1575 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#5415, A4×#3003, #72226284, … |
| maximal normal subgroup of | A4×#3003, #72226284, #72226317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084696);