Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C59×#452 ⋊ C2 |
| Sylow | C59 ⋊ #3222 |
396 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=e,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=fg,h^c=h^58577 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3222, C2×#21435166, #29460097, … |
| maximal normal subgroup of | D59×#3222, C2×#21435166, #29460097, … |
| maximal quotient of | #28598061, #28598481, #28599273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15580);