Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #1533 |
248 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 77 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=e,d^2=g,e^2=f,b^a=bd,c^a=cg,d^a=df,h^a=h^58,d^b=dg,e^b=efg838 conjugacy classes — view the full character table.
| maximal subgroup of | #28476415, #28476416, #28476457, … |
| maximal normal subgroup of | #28476415, #28476416, #28476457, … |
| maximal quotient of | #28476766, #28476778, #28476804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3134);