Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C4×D4×D12 |
| Fitting | C3×C42×D4 ⋊ C2 |
| Sylow | C3 ⋊ C4×D42 |
4804 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
180 conjugacy classes — view the full character table.
| maximal quotient of | #72226114 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 329359);