Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #2214 |
150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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,b^2=dg,d^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,h^a=h^42,e^c=ef,f^c=fg611 conjugacy classes — view the full character table.
| maximal subgroup of | #25010000, #25010002, #25010005, … |
| maximal normal subgroup of | #25010000, #25010002, #25010005, … |
| maximal quotient of | #25010755, #25010762, #25010779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6591);