Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#69006 |
| Fitting | C2×C3×#343 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1907 |
1826 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171492);