Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #103×Dic67 |
| Sylow | C67 ⋊ C4×#103 |
332 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#103×D67, C2×#103×Dic67, C4×#16863391, … |
| maximal normal subgroup of | C4×#103×D67, C2×#103×Dic67, C4×#16863391, … |
| maximal quotient of | Q8⋊C8×Dic67, #30746460, #30746465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4332);