Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C43×#500 ⋊ C2 |
| Sylow | C43 ⋊ #2243 |
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^a=h^42,c^b=cg,h^b=h^42,h^c=h^42488 conjugacy classes — view the full character table.
| maximal subgroup of | #25010431, #25010432, #25010438, … |
| maximal normal subgroup of | #25010431, #25010432, #25010438, … |
| maximal quotient of | #25012984, #25014526, #25014533, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6749);