Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #3135 |
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,c^b=cg,h^b=h^58,h^c=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | #28483636, #28483638, #28483650, … |
| maximal normal subgroup of | #28483636, #28483638, #28483650, … |
| maximal quotient of | #28588890, #28591331, #28592351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14855);