Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #3233 |
332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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=eg,c^2=e,d^2=g,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 | #28566208, #28566214, #28566238, … |
| maximal normal subgroup of | #28566208, #28566214, #28566238, … |
| maximal quotient of | #28598194, #28598391, #28599232, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15685);