Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C43 ⋊ #2049 |
254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,f^c=fg,h^c=h^42485 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2049, C2×#19135872, #25124440, … |
| maximal normal subgroup of | D43×#2049, C2×#19135872, #25124440, … |
| maximal quotient of | #25000188, #25000195, #25000202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5787);