Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1385 |
124 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=e,c^2=f,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^42,d^b=dg872 conjugacy classes — view the full character table.
| maximal subgroup of | #24984170, #24984171, #24984173, … |
| maximal normal subgroup of | #24984170, #24984171, #24984173, … |
| maximal quotient of | #24983473, #24983518, #24983643, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2614);