Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #3222 |
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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=g,b^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^58,c^b=ce,d^b=dg,f^c=fg664 conjugacy classes — view the full character table.
| maximal subgroup of | #28509083, #28509086, #28509098, … |
| maximal normal subgroup of | #28509083, #28509086, #28509098, … |
| maximal quotient of | #28598063, #28598487, #28599279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15582);