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 ⋊ #3105 |
454 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,h^b=h^58,f^c=fg850 conjugacy classes — view the full character table.
| maximal subgroup of | #28558656, #28558660, #28558698, … |
| maximal normal subgroup of | #28558656, #28558660, #28558698, … |
| maximal quotient of | #28588692, #28591630, #28591631, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14561);