Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C7 |
| direct product | Q16×C7⋊D7 |
| Fitting | C72×Q16 ⋊ C2 |
| Sylow | C72 ⋊ C2×Q16 |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 784 |
182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 723);