Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1960 |
308 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 113 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=df,c^2=eg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^42,c^b=cg,h^b=h^42620 conjugacy classes — view the full character table.
| maximal subgroup of | #24984390, #24988990, #24988992, … |
| maximal normal subgroup of | #24984390, #24988990, #24988992, … |
| maximal quotient of | #24995388, #24995414, #24995594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5331);