Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C43×#448 ⋊ C2 |
| Sylow | C43 ⋊ #3225 |
376 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^42,f^c=fg,h^c=h^42425 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3225, C2×#19145702, #25968003, … |
| maximal normal subgroup of | D43×#3225, C2×#19145702, #25968003, … |
| maximal quotient of | #25105978, #25106361, #25107201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15617);