Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3166 |
348 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 165 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=eg,c^2=f,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,d^c=dg872 conjugacy classes — view the full character table.
| maximal subgroup of | #24994220, #24997509, #24997511, … |
| maximal normal subgroup of | #24994220, #24997509, #24997511, … |
| maximal quotient of | #25097032, #25099987, #25101186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15062);