Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863801 |
| Sylow | C67 ⋊ C2×#500 |
424 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2156 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30751086, #30751088, #30755053, … |
| maximal normal subgroup of | #30751086, #30751088, #30755053, … |
| maximal quotient of | C2×#22560369, C2×#22560942, C2×#22561170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15018);