Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #2219 |
150 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 51 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=df,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,c^b=cg,h^b=h^42488 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2219, C2×#19136701, #25251061, … |
| maximal normal subgroup of | D43×#2219, C2×#19136701, #25251061, … |
| maximal quotient of | #25010823, #25010874, #25010942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6616);