Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #3105 |
454 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 123 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=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,f^c=fg,h^d=h^58589 conjugacy classes — view the full character table.
| maximal subgroup of | #28561012, #28561014, #28561034, … |
| maximal normal subgroup of | #28561012, #28561014, #28561034, … |
| maximal quotient of | #28588689, #28591621, #28591669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14552);