Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C43 ⋊ #1356 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=g,c^2=f,d^2=e,e^2=g,b^a=bc,c^a=ce,f^a=fg,c^b=cf,d^b=defg,e^b=eg,h^b=h^42,d^c=dg482 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1356, C2×#19132629, #25007772, … |
| maximal normal subgroup of | D43×#1356, C2×#19132629, #25007772, … |
| maximal quotient of | #24983376, #24983412, #24983765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2544);