Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1759 |
320 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 117 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=f,c^2=e,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^42,c^b=cg,h^c=h^42632 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1759, C2×#19134407, C4×#14582914, … |
| maximal normal subgroup of | D43×#1759, C2×#19134407, C4×#14582914, … |
| maximal quotient of | #24987201, #24987206, #24987221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4322);