Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D137⋊#444 |
| Fitting | #135×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×#444 |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^7,137|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^37,e^b=eg,h^c=h^100,h^d=h^136,h^f=h^136520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21281);