Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #2217 |
164 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 55 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^2=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^b=h^42500 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2217, C2×#19136689, #25251031, … |
| maximal normal subgroup of | D43×#2217, C2×#19136689, #25251031, … |
| maximal quotient of | #25010811, #25010862, #25010930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6604);