Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | A4×#334 |
| unambiguous semidirect product | (C22×#334)⋊C3 |
| Fitting, Sylow | C22×#334 ⋊ C3 |
247 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#1580, A4×#1368, S4×#334, … |
| maximal normal subgroup of | A4×#1580, A4×#1368, S4×#334, … |
| maximal quotient of | A4×#1368, A4×#1369 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083775);