Finite Group DatabasebetaFinite Group Databasebeta| order | 21536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C673 ⋊ C2 |
| Sylow | C673 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5384 |
Polycyclic presentation:
2^5,673|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^672,d^b=de,f^c=f^6722363 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21536, 173);