Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C59×#447 ⋊ C2 |
| Sylow | C59 ⋊ #3224 |
408 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^58,f^c=fg577 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3224, C2×#21435186, #29460092, … |
| maximal normal subgroup of | D59×#3224, C2×#21435186, #29460092, … |
| maximal quotient of | #28598059, #28598453, #28599303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15600);