Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×D16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2250 |
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,c^b=cg,h^c=h^66752 conjugacy classes — view the full character table.
| maximal subgroup of | #2250×D67, C2×#22562472, #31011251, … |
| maximal normal subgroup of | #2250×D67, C2×#22562472, #31011251, … |
| maximal quotient of | #30770498, #30770500, #30770510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6773);