Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #459×C137 ⋊ C2 |
| Sylow | C137 ⋊ #3035 |
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8768 |
Polycyclic presentation:
2^7,137|b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,f^c=fg,h^d=h^1361330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 13958);