Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C43×#473 ⋊ C2 |
| Sylow | C43 ⋊ #2195 |
206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 206 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,c^2=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,d^b=df,f^b=fg,h^b=h^42,e^c=eg359 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2195, C2×#19136571, #25250551, … |
| maximal normal subgroup of | D43×#2195, C2×#19136571, #25250551, … |
| maximal quotient of | #25008749, #25008754, #25009093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6486);