Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q32×Dic67 |
| Sylow | C67 ⋊ C4×Q32 |
150 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | #30776407, SD64×Dic67, #30776414, … |
| maximal normal subgroup of | #30776407, SD64×Dic67, #30776414, … |
| maximal quotient of | Q32×C67⋊C8, #30767748, #30767822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6369);