Finite Group DatabasebetaFinite Group Databasebeta| order | 20512 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C641 ⋊ C2 |
| Sylow | C641 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5128 |
Polycyclic presentation:
2^5,641|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^640,d^b=de,f^b=f^6403211 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20512, 174);