Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #1830 |
236 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 81 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=f,b^2=g,c^2=d,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^b=fg,e^c=eg,h^c=h^58667 conjugacy classes — view the full character table.
| maximal subgroup of | #28504321, #28504323, #28504325, … |
| maximal normal subgroup of | #28504321, #28504323, #28504325, … |
| maximal quotient of | #28482149, #28482155, #28482209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4622);