Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #2988 |
432 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8384 |
Polycyclic presentation:
2^7,131|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,h^b=h^130,h^c=h^130,h^d=h^1302668 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 13620);