Finite Group DatabasebetaFinite Group Databasebeta| order | 32288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C1009 ⋊ C2 |
| Sylow | C1009 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8072 |
Polycyclic presentation:
2^5,1009|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^1008,d^b=de5051 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32288, 172);