Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#16863806 |
| Sylow | C67 ⋊ C2×#501 |
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
956 conjugacy classes — view the full character table.
| maximal subgroup of | #30750751, #30750753, #30757135, … |
| maximal normal subgroup of | #30750751, #30750753, #30757135, … |
| maximal quotient of | C2×#22560378, C2×#22560944, C2×#22560949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15030);