Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1998 |
228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 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=def,c^2=eg,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^42,d^b=dg,f^b=fg,h^b=h^42620 conjugacy classes — view the full character table.
| maximal subgroup of | #24988910, #24988912, #24988917, … |
| maximal normal subgroup of | #24988910, #24988912, #24988917, … |
| maximal quotient of | #24996646, #24996651, #24996698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5504);