Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C43 ⋊ #1342 |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=g,c^2=fg,d^2=g,e^2=g,f^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^42,c^b=cf,d^b=defg,e^b=eg,f^b=fg,d^c=dg356 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1342, C2×#19132589, #25006759, … |
| maximal normal subgroup of | D43×#1342, C2×#19132589, #25006759, … |
| maximal quotient of | #24983300, #24983303, #24983312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2504);