Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C59 ⋊ #1609 |
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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=g,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^58,d^b=df,e^b=eg,d^c=dg,h^c=h^58574 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1609, C2×#21423094, #28560847, … |
| maximal normal subgroup of | D59×#1609, C2×#21423094, #28560847, … |
| maximal quotient of | #28477726, #28477735, #28477754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3508);