Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C131 ⋊ #2316 |
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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=g,b^2=e,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^1301864 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 7127);