Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #3299 |
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 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|a^2=eg,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,d^b=de,f^c=fg760 conjugacy classes — view the full character table.
| maximal subgroup of | #28578422, #28578430, #28578437, … |
| maximal normal subgroup of | #28578422, #28578430, #28578437, … |
| maximal quotient of | D4×#14273651, #28604923, #28605881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16386);