Finite Group DatabasebetaFinite Group Databasebeta| order | 32288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C1009 ⋊ M32 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16144 |
Polycyclic presentation:
2^5,1009|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^762,f^b=f^1008,f^c=f^469,f^d=f^1008524 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32288, 243);