Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#544 ⋊ C2 |
| Sylow | C43 ⋊ #3243 |
320 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|b^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^42,c^b=ce,d^b=dg,f^c=fg488 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3243, C2×#19145878, #25968849, … |
| maximal normal subgroup of | D43×#3243, C2×#19145878, #25968849, … |
| maximal quotient of | #25106148, #25106370, #25107198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15793);