Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3162 |
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|a^2=e,b^2=e,c^2=f,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,h^b=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #30774913, #30774914, #30774918, … |
| maximal normal subgroup of | #30774913, #30774914, #30774918, … |
| maximal quotient of | #30856252, #30859182, #30859183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15033);