Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4 |
| direct product | C4×D3×#131 |
| Fitting | C3×C4×#131 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×#131 |
3366 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33326 |
| maximal normal subgroup of | D3×#33326 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1032968);