Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C43 ⋊ #2188 |
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^42491 conjugacy classes — view the full character table.
| maximal subgroup of | #25008716, #25008717, #25008722, … |
| maximal normal subgroup of | #25008716, #25008717, #25008722, … |
| maximal quotient of | #25008715, #25009059, #25009819, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6443);