Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #346×C131 ⋊ C2 |
| Sylow | C131 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 113 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=d,b^2=e,d^2=f,f^2=g,c^a=cg,h^b=h^130,h^c=h^1302680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 6103);