Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C43 ⋊ #1788 |
612 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=f,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^42,d^b=dg878 conjugacy classes — view the full character table.
| maximal subgroup of | #24988785, #24988786, #24988799, … |
| maximal normal subgroup of | #24988785, #24988786, #24988799, … |
| maximal quotient of | #24987973, #24987986, #24988047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4450);