Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C4×C8×C137 ⋊ C4 |
| Sylow | C137 ⋊ #1744 |
296 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^7,137|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^b=h^100,h^f=h^1361168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 20223);