Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #125×C137 ⋊ C4 |
| Sylow | C137 ⋊ #2382 |
408 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 152 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=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^100,c^b=cef,d^b=de,h^g=h^136514 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21056);