Finite Group DatabasebetaFinite Group Databasebeta| order | 21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#19129602 |
| unambiguous semidirect product | (C2×#19129602)⋊C2 |
| Fitting | C22×C1361 ⋊ C4 |
| Sylow | C1361 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5444 |
Polycyclic presentation:
2^4,1361|a^2=d,b^a=bc,e^a=e^747,e^d=e^13601370 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21776, 45);