Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of #4466 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C42 |
| direct product | C4×#4466 |
| Sylow | C3 ⋊ C4×#347 |
418 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#347, #72225843, #72225844, … |
| maximal normal subgroup of | C4×D3×#347, #72225843, #72225844, … |
| maximal quotient of | #72225843 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84396);