Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | SD32×Dic67 |
| Sylow | C67 ⋊ C4×SD32 |
162 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
770 conjugacy classes — view the full character table.
| maximal subgroup of | C4×SD32×D67, C2×SD32×Dic67, C4×#16863827, … |
| maximal normal subgroup of | C4×SD32×D67, C2×SD32×Dic67, C4×#16863827, … |
| maximal quotient of | SD32×C67⋊C8, #30767734, #30767741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6363);