Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#450 ⋊ C2 |
| Sylow | C43 ⋊ #3264 |
568 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^42,d^b=de,e^b=eg,h^b=h^42,e^d=eg428 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3264, C2×#19146079, #25971667, … |
| maximal normal subgroup of | D43×#3264, C2×#19146079, #25971667, … |
| maximal quotient of | #25085948, #25086068, #25086188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15994);