Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#71539 |
| Sylow | C3 ⋊ C2×#1462 |
2790 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #72255480, C2×D3×#1462, #72255493 |
| maximal normal subgroup of | #72255480, C2×D3×#1462, #72255493 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 135405);