Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3232 |
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 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=eg,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,f^c=fg,h^c=h^42620 conjugacy classes — view the full character table.
| maximal subgroup of | #24993091, #24993093, #25070683, … |
| maximal normal subgroup of | #24993091, #24993093, #25070683, … |
| maximal quotient of | #25106095, #25106290, #25107123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15674);