Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×A4×D8 |
| unambiguous semidirect product | (C22×C4×D8)⋊C3 |
| Fitting, Sylow | C22×C4×D8 ⋊ C3 |
839 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 839 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#2177, A4×#1580, C4×D8×S4, … |
| maximal normal subgroup of | A4×#2177, A4×#1580, C4×D8×S4, … |
| maximal quotient of | A4×#2179, A4×#2177 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084639);