Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #125×C137 ⋊ C4 |
| Sylow | C137 ⋊ #1414 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^7,137|a^2=d,b^2=f,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^100,c^b=cfg,d^b=defg,e^b=eg,d^c=dfg,e^d=eg,h^d=h^136493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 19655);