Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #2185 |
226 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 57 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=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^58667 conjugacy classes — view the full character table.
| maximal subgroup of | #28500803, #28500804, #28500814, … |
| maximal normal subgroup of | #28500803, #28500804, #28500814, … |
| maximal quotient of | #28500790, #28501134, #28501894, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6426);