Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×#69106 |
| Fitting | C2×C3×C22⋊C16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2112 |
1406 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322235);