Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C32×C137 ⋊ C4 |
| Sylow | C137 ⋊ #1398 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^7,137|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bf,d^a=dg,c^b=cg,h^b=h^37,h^d=h^1361132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 19620);