Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C43×#340 ⋊ C2 |
| Sylow | C43 ⋊ #1347 |
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=d,c^2=fg,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^42617 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1347, C2×#19132603, #25006823, … |
| maximal normal subgroup of | D43×#1347, C2×#19132603, #25006823, … |
| maximal quotient of | #24983269, #24983278, #24983305, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2518);