Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×#10621883 |
| Sylow | C43 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
896 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#10621883, #25008366, #25008368, … |
| maximal normal subgroup of | C16×#10621883, #25008366, #25008368, … |
| maximal quotient of | C8×#13063246, C8×#13063248, C8×#13063256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3308);