Finite Group DatabasebetaFinite Group Databasebeta| order | 21536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C673 ⋊ C4 |
| Sylow | C673 ⋊ #103 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5384 |
Polycyclic presentation:
2^5,673|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^58,c^b=ce,f^d=f^672854 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21536, 209);