Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C43×#436 ⋊ C2 |
| Sylow | C43 ⋊ #1589 |
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cg,d^b=df,h^b=h^42632 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1589, C2×#19133478, #25066343, … |
| maximal normal subgroup of | D43×#1589, C2×#19133478, #25066343, … |
| maximal quotient of | #24987415, #24987419, #24987832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3393);