Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #2175 |
160 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 65 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,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^66,d^b=df,f^b=fg,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #2175×D67, C2×#22562074, #31009136, … |
| maximal normal subgroup of | #2175×D67, C2×#22562074, #31009136, … |
| maximal quotient of | #30767571, #30767762, #30767769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6375);