Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3246 |
392 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 137 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=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^42,c^b=ce,f^c=fg620 conjugacy classes — view the full character table.
| maximal subgroup of | #24997534, #24997536, #24997546, … |
| maximal normal subgroup of | #24997534, #24997536, #24997546, … |
| maximal quotient of | #25106477, #25106480, #25106967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15826);