Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C43 ⋊ #1364 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=e,c^2=fg,d^2=efg,f^2=g,b^a=bc,c^a=ce,h^a=h^42,c^b=cf,d^b=def,f^b=fg491 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1364, C2×#19132650, #25007881, … |
| maximal normal subgroup of | D43×#1364, C2×#19132650, #25007881, … |
| maximal quotient of | #24983385, #24983782, #24984248, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2565);