Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3285 |
482 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^42,d^b=de,e^b=eg,h^b=h^42,e^d=eg,h^d=h^42875 conjugacy classes — view the full character table.
| maximal subgroup of | #25253066, #25253075, #25253126, … |
| maximal normal subgroup of | #25253066, #25253075, #25253126, … |
| maximal quotient of | #25087146, #25087161, #25087176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16253);