Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | SD16⋊(C43⋊C8) |
| Sylow | C43 ⋊ SD16⋊C8 |
176 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 87 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=e,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^42,d^b=df,h^c=h^42632 conjugacy classes — view the full character table.
| maximal subgroup of | D43×SD16⋊C8, C2×SD16⋊(C43⋊C8), #25065998, … |
| maximal normal subgroup of | D43×SD16⋊C8, C2×SD16⋊(C43⋊C8), #25065998, … |
| maximal quotient of | #24987376, #24987383, #24987848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3323);