Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#16863689 |
| Sylow | C67 ⋊ C2×#477 |
416 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 416 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.
962 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16863689, #30863423, #30863496, … |
| maximal normal subgroup of | C4×#16863689, #30863423, #30863496, … |
| maximal quotient of | C2×#22560212, C2×#22560461, C2×#22560465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14279);