Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16863717 |
| Sylow | C67 ⋊ C2×#482 |
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
962 conjugacy classes — view the full character table.
| maximal subgroup of | #30752156, #30752162, C4×#16863717, … |
| maximal normal subgroup of | #30752156, #30752162, C4×#16863717, … |
| maximal quotient of | C2×#22560301, C2×#22560406, C2×#22560532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14391);