Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #366×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2159 |
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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,b^2=df,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #2159×D67, C2×#22561994, #31008867, … |
| maximal normal subgroup of | #2159×D67, C2×#22561994, #31008867, … |
| maximal quotient of | #30767417, #30767481, #30767523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6295);