Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q8×#14582115 |
| Fitting | Q8×C337 ⋊ C8 |
| Sylow | C337 ⋊ C8×Q8 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2696 |
250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1664);