Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#5028 |
| Fitting | C3×C42×Q8 ⋊ C2 |
| Sylow | C3 ⋊ C4×#464 |
1016 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 175803);