Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C43 ⋊ #2196 |
354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|b^a=bd,c^a=ce,f^a=fg,h^a=h^42,e^b=efg,d^c=df,h^c=h^42,e^d=eg293 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2196, C2×#19136580, #25250617, … |
| maximal normal subgroup of | D43×#2196, C2×#19136580, #25250617, … |
| maximal quotient of | #25008627, #25008628, #25008661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6495);