Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C137 ⋊ C8 |
| Sylow | C137 ⋊ #2982 |
396 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^7,137|a^2=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,h^a=h^127,c^b=ce,h^f=h^100,h^g=h^136238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21753);