Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C42×C137 ⋊ C8 |
| Sylow | C137 ⋊ #1842 |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^7,137|a^2=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^127,h^f=h^100,h^g=h^136328 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21654);