Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C43 ⋊ #2231 |
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 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=df,b^2=dg,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,h^a=h^42,e^c=efg,f^c=fg611 conjugacy classes — view the full character table.
| maximal subgroup of | #25010988, #25010990, #25010993, … |
| maximal normal subgroup of | #25010988, #25010990, #25010993, … |
| maximal quotient of | #25012703, #25013294, #25014296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6686);