Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×M16×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×#344 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^7,137|a^2=e,b^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^37,e^b=eg,h^b=h^100,h^c=h^136,h^e=h^136,h^f=h^136724 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 20222);