Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C137 ⋊ C8 |
| Sylow | C137 ⋊ #1325 |
134 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1096 |
Polycyclic presentation:
2^7,137|a^2=d,b^2=eg,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^127,d^b=deg,d^c=dg,h^d=h^100,h^f=h^136298 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21547);