Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#452 ⋊ C2 |
| Sylow | C43 ⋊ #3271 |
488 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|b^2=g,c^2=g,d^2=g,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×#3271, C2×#19146184, #25971667, … |
| maximal normal subgroup of | D43×#3271, C2×#19146184, #25971667, … |
| maximal quotient of | #25086053, #25086173, #25086398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16099);