Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#2048 |
| Fitting | C3×#2048 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2048 |
1450 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
69 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#30434, C2×D3×#2048 |
| maximal normal subgroup of | D3×#30434, C2×D3×#2048 |
| maximal quotient of | C2×D3×#2048, #72248319, #72248331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 197394);