Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3178 |
350 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=dg,h^d=h^42368 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3178, C2×#19145256, #25966490, … |
| maximal normal subgroup of | D43×#3178, C2×#19145256, #25966490, … |
| maximal quotient of | #25097171, #25100880, #25100900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15171);