Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1846 |
248 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 117 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=f,b^2=d,c^2=eg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^58,h^c=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | #28504738, #28504739, #28504743, … |
| maximal normal subgroup of | #28504738, #28504739, #28504743, … |
| maximal quotient of | #28482433, #28482448, #28482457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4673);