Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #384×C137 ⋊ C2 |
| Sylow | C137 ⋊ #2285 |
656 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 261 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|a^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,h^b=h^136,h^d=h^1361960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 6915);