Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #484×C137 ⋊ C2 |
| Sylow | C137 ⋊ #3120 |
372 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8768 |
Polycyclic presentation:
2^7,137|a^2=g,b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^c=h^136,h^d=h^1361324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 14719);