Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | A4×#322 |
| unambiguous semidirect product | (C22×#322)⋊C3 |
| Fitting, Sylow | C22×#322 ⋊ C3 |
307 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#1580, A4×#1313, S4×#322, … |
| maximal normal subgroup of | A4×#1580, A4×#1313, S4×#322, … |
| maximal quotient of | A4×#1313 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083727);