Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#467 ⋊ C2 |
| Sylow | C43 ⋊ #3344 |
344 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,c^b=cg,d^b=de,h^b=h^42,f^c=fg,h^c=h^42491 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3344, C2×#19147056, #25975259, … |
| maximal normal subgroup of | D43×#3344, C2×#19147056, #25975259, … |
| maximal quotient of | #25112891, #25112981, #25114277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16971);