Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #3137 |
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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,b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^58,d^b=dg,h^b=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | #28658649, #28658653, #28658679, … |
| maximal normal subgroup of | #28658649, #28658653, #28658679, … |
| maximal quotient of | #28588899, #28591341, #28591346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14879);