Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #335×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1567 |
184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 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=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^c=h^66968 conjugacy classes — view the full character table.
| maximal subgroup of | #30765856, #30765860, #30765869, … |
| maximal normal subgroup of | #30765856, #30765860, #30765869, … |
| maximal quotient of | #30745295, #30747023, #30747026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 3267);