Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #3250 |
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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,d^a=de,f^a=fg,c^b=ce,f^c=fg,h^d=h^58670 conjugacy classes — view the full character table.
| maximal subgroup of | #28501138, #28501142, #28501155, … |
| maximal normal subgroup of | #28501138, #28501142, #28501155, … |
| maximal quotient of | #28598578, #28599065, #28600765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15856);