Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#16863161 |
| Sylow | C67 ⋊ C2×#341 |
392 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742977, #30742979, #30742983, … |
| maximal normal subgroup of | #30742977, #30742979, #30742983, … |
| maximal quotient of | C2×#22558044, #30745290, #30745297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4234);