Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #346×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2251 |
178 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 61 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=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^66,c^b=cg1346 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30769327, #30769328, #30769334, … |
| maximal normal subgroup of | #30769327, #30769328, #30769334, … |
| maximal quotient of | #30770506, #30770511, #30770530, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6781);