Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#41×C137 ⋊ C4 |
| Sylow | C137 ⋊ #2896 |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^7,137|a^2=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^100,e^b=eg,h^f=h^136724 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21130);