Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C43×#413 ⋊ C2 |
| Sylow | C43 ⋊ #2889 |
704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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=g,f^2=g,b^a=be,e^a=eg,f^b=fg,d^c=dg,h^c=h^42,h^d=h^42503 conjugacy classes — view the full character table.
| maximal subgroup of | #25014153, #25014155, #25014157, … |
| maximal normal subgroup of | #25014153, #25014155, #25014157, … |
| maximal quotient of | #25062418, #25062420, #25062423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12991);