Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#427 ⋊ C2 |
| Sylow | C59 ⋊ #3076 |
388 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^58,f^c=fg,h^c=h^58850 conjugacy classes — view the full character table.
| maximal subgroup of | #28596517, #28596518, #28596528, … |
| maximal normal subgroup of | #28596517, #28596518, #28596528, … |
| maximal quotient of | #28588161, #28589631, #28589638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14296);