Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C67 ⋊ #2201 |
226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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=g,c^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cg,e^b=efg,d^c=df,h^c=h^66,e^d=eg545 conjugacy classes — view the full character table.
| maximal subgroup of | #2201×D67, C2×#22562220, #31009878, … |
| maximal normal subgroup of | #2201×D67, C2×#22562220, #31009878, … |
| maximal quotient of | #30767887, #30767888, #30767921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6521);