Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#69130 |
| Fitting | C2×C3×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C3 ⋊ C2×#2196 |
1956 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2196, #72245157, #72245318, … |
| maximal normal subgroup of | C2×D3×#2196, #72245157, #72245318, … |
| maximal quotient of | #72245318 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323570);