Finite Group DatabasebetaFinite Group Databasebeta| order | 21536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#14582089 |
| unambiguous semidirect product | D673⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×#14582089)⋊C22 |
| Fitting | C23×C673 ⋊ C4 |
| Sylow | C673 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5384 |
1364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21536, 223);