Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D16×Dic43 |
| Sylow | C43 ⋊ C4×D16 |
174 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
506 conjugacy classes — view the full character table.
| maximal subgroup of | #25017168, D32×Dic43, SD64×Dic43, … |
| maximal normal subgroup of | #25017168, D32×Dic43, SD64×Dic43, … |
| maximal quotient of | D16×C43⋊C8, #25008493, #25008576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6357);