Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #2240 |
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^b=h^66,h^c=h^66764 conjugacy classes — view the full character table.
| maximal subgroup of | #30769421, #30769422, #30769428, … |
| maximal normal subgroup of | #30769421, #30769422, #30769428, … |
| maximal quotient of | #30772210, #30773750, #30774046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6733);