Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#13062438 |
| unambiguous semidirect product | D337⋊(C2×C22⋊C4) |
| unambiguous semidirect product | (C2×#13062438)⋊C23 |
| Fitting | C24×C337 ⋊ C4 |
| Sylow | C337 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5392 |
1384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1610);