Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #458×C131 ⋊ C2 |
| Sylow | C131 ⋊ #2197 |
258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2096 |
Polycyclic presentation:
2^7,131|b^2=g,b^a=bd,c^a=ce,f^a=fg,e^b=efg,d^c=df,h^c=h^130,e^d=eg1060 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 6497);