Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D3×#1595 |
| Fitting | C3×#1595 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1595 |
2040 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
69 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#18162, #72252349 |
| maximal normal subgroup of | D3×#18162 |
| maximal quotient of | #72252349, D3×#9914 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 141629);