Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#467 ⋊ C2 |
| Sylow | C59 ⋊ #3191 |
424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^58,c^b=ce,f^c=fg,h^c=h^58,h^d=h^58670 conjugacy classes — view the full character table.
| maximal subgroup of | #28500796, #28500800, #28500813, … |
| maximal normal subgroup of | #28500796, #28500800, #28500813, … |
| maximal quotient of | #28597705, #28598954, #28599847, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15304);