Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of #6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#6400 |
| Fitting | C72×D8 ⋊ C2 |
| Sylow | C72 ⋊ D16 |
89 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 269);