Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1531 |
212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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=e,b^2=f,c^2=g,d^2=g,e^2=f,b^a=bd,c^a=cf,d^a=df,h^a=h^42,d^b=dg,e^b=efg,h^b=h^42620 conjugacy classes — view the full character table.
| maximal subgroup of | #24988487, #24988488, #24988494, … |
| maximal normal subgroup of | #24988487, #24988488, #24988494, … |
| maximal quotient of | #24984615, #24984658, #24984671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3126);