Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3163 |
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 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,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^66,d^b=dg,h^b=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #30774466, #30774472, #30774952, … |
| maximal normal subgroup of | #30774466, #30774472, #30774952, … |
| maximal quotient of | #30856275, #30859192, #30859203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15042);