Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C43 ⋊ #2255 |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=d,c^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^42,c^b=cg,h^c=h^42488 conjugacy classes — view the full character table.
| maximal subgroup of | #25010601, #25010602, #25010608, … |
| maximal normal subgroup of | #25010601, #25010602, #25010608, … |
| maximal quotient of | #25013043, #25014634, #25014639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6797);