Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#442 ⋊ C2 |
| Sylow | C43 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=f,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^42,e^b=eg,h^c=h^42,h^d=h^42506 conjugacy classes — view the full character table.
| maximal subgroup of | C4×AGL(1,ℤ/8)×D43, C2×#19143406, C4×#14583695, … |
| maximal normal subgroup of | C4×AGL(1,ℤ/8)×D43, C2×#19143406, C4×#14583695, … |
| maximal quotient of | #25066014, #25066183, #25066199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13321);