Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of D112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D112 |
| Fitting | C72×C16 ⋊ C2 |
| Sylow | C72 ⋊ D16 |
71 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
413 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 243);