Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #1820 |
300 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 85 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,b^2=g,c^2=d,b^a=bd,c^a=ce,e^a=eg,f^c=fg,h^c=h^42620 conjugacy classes — view the full character table.
| maximal subgroup of | #24983967, #24988774, #24988777, … |
| maximal normal subgroup of | #24983967, #24988774, #24988777, … |
| maximal quotient of | #24989921, #24989927, #24989933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4585);