Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #2161 |
140 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 81 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=e,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,h^b=h^42620 conjugacy classes — view the full character table.
| maximal subgroup of | #25012023, #25012025, #25012026, … |
| maximal normal subgroup of | #25012023, #25012025, #25012026, … |
| maximal quotient of | #25008184, #25008187, #25008248, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6304);