Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #1467 |
236 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 89 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,b^2=f,c^2=fg,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^58,e^b=ef1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475804, #28475805, #28476003, … |
| maximal normal subgroup of | #28475804, #28475805, #28476003, … |
| maximal quotient of | #28476882, #28476895, #28476908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2854);