Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#529 ⋊ C2 |
| Sylow | C59 ⋊ #3247 |
398 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^58,c^b=ce,f^c=fg844 conjugacy classes — view the full character table.
| maximal subgroup of | #28565785, #28565791, #28565800, … |
| maximal normal subgroup of | #28565785, #28565791, #28565800, … |
| maximal quotient of | #28598594, #28598597, #28599078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15836);