Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#451 ⋊ C2 |
| Sylow | C59 ⋊ #3277 |
476 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^58,c^b=cg,d^b=de,e^b=eg,h^c=h^58,e^d=eg,h^d=h^58580 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3277, C2×#21435753, #29463862, … |
| maximal normal subgroup of | D59×#3277, C2×#21435753, #29463862, … |
| maximal quotient of | #28580013, #28580126, #28580127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16167);