Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #3227 |
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|b^2=e,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,f^c=fg,h^c=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | #28485204, #28485206, #28485330, … |
| maximal normal subgroup of | #28485204, #28485206, #28485330, … |
| maximal quotient of | #28598174, #28598366, #28599201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15635);