Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | #341×D67 |
| Fitting | #341×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#341 |
392 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #1349×D67, #1350×D67, #30766082, … |
| maximal normal subgroup of | #1349×D67, #1350×D67, #30766082, … |
| maximal quotient of | #1277×D67, #30745288, #30745295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4232);