Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3168 |
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|b^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^c=h^42,h^d=h^42506 conjugacy classes — view the full character table.
| maximal subgroup of | #25006998, #25007019, #25007032, … |
| maximal normal subgroup of | #25006998, #25007019, #25007032, … |
| maximal quotient of | #25097139, #25100805, #25100814, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15075);