Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #2085 |
214 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 85 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=eg,b^2=d,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^66,c^b=cf,f^b=fg,f^c=fg956 conjugacy classes — view the full character table.
| maximal subgroup of | #2085×D67, C2×#22561693, #30884809, … |
| maximal normal subgroup of | #2085×D67, C2×#22561693, #30884809, … |
| maximal quotient of | #30760774, #30760781, #30760788, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5994);