Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C59×#423 ⋊ C2 |
| Sylow | C59 ⋊ #1495 |
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cfg,d^b=df,h^b=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | #28480986, #28480991, #28480993, … |
| maximal normal subgroup of | #28480986, #28480991, #28480993, … |
| maximal quotient of | #28477206, #28477211, #28477216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2973);