Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | A4×#367 |
| unambiguous semidirect product | (C22×#367)⋊C3 |
| Fitting, Sylow | C22×#367 ⋊ C3 |
207 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 207 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#2177, #72342756, #72342759, … |
| maximal normal subgroup of | A4×#2177, #72342756, #72342759, … |
| maximal quotient of | A4×#1426 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084074);