Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #2214 |
150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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=g,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,h^a=h^66,e^c=ef,f^c=fg947 conjugacy classes — view the full character table.
| maximal subgroup of | #30769234, #30769236, #30769239, … |
| maximal normal subgroup of | #30769234, #30769236, #30769239, … |
| maximal quotient of | #30769989, #30769996, #30770013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6591);