Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of #67526 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#67526 |
| Fitting | C2×C3×C22⋊C16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1347 |
558 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 79788);