Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#69143 |
| Fitting | C2×C3×#352 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2121 |
1494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2121, #72248423, #72248425, … |
| maximal normal subgroup of | C2×D3×#2121, #72248423, #72248425, … |
| maximal quotient of | #72255137 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322294);