Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3305 |
408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 408 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=eg,b^2=g,c^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,d^b=de,h^b=h^58,f^c=fg,h^d=h^58847 conjugacy classes — view the full character table.
| maximal subgroup of | #28578450, #28578458, #28578465, … |
| maximal normal subgroup of | #28578450, #28578458, #28578465, … |
| maximal quotient of | #28604160, #28604957, #28605857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16462);