Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C43×#483 ⋊ C2 |
| Sylow | C43 ⋊ #1608 |
228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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=g,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=eg,d^c=dg,h^c=h^42422 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1608, C2×#19133584, #25068750, … |
| maximal normal subgroup of | D43×#1608, C2×#19133584, #25068750, … |
| maximal quotient of | #24985623, #24985625, #24985651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3499);