Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3062 |
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,d^c=dg,h^c=h^58670 conjugacy classes — view the full character table.
| maximal subgroup of | #28636655, #28636658, #28636670, … |
| maximal normal subgroup of | #28636655, #28636658, #28636670, … |
| maximal quotient of | #28572167, #28572189, #28572211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14184);