Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #493×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2213 |
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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=dg,d^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,e^c=ef,f^c=fg,h^c=h^66749 conjugacy classes — view the full character table.
| maximal subgroup of | #30769222, #30769223, #30769227, … |
| maximal normal subgroup of | #30769222, #30769223, #30769227, … |
| maximal quotient of | #30769958, #30769965, #30770000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6583);