Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1945 |
208 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 93 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=f,b^2=f,c^2=e,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^421388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24983381, #24983383, #25013217, … |
| maximal normal subgroup of | #24983381, #24983383, #25013217, … |
| maximal quotient of | #24995134, #24995139, #24995164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5258);