Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C22 |
| direct product | A4×#346 |
| unambiguous semidirect product | (C22×#346)⋊C3 |
| Fitting, Sylow | C22×#346 ⋊ C3 |
247 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 75 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 | #72342674, A4×#2179, S4×#346, … |
| maximal normal subgroup of | #72342674, A4×#2179, S4×#346, … |
| maximal quotient of | A4×#1398 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084032);