Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#440 ⋊ C2 |
| Sylow | C59 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=f,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^c=h^58,h^d=h^58682 conjugacy classes — view the full character table.
| maximal subgroup of | C4×AGL(1,ℤ/8)×D59, C2×#21432901, #29452772, … |
| maximal normal subgroup of | C4×AGL(1,ℤ/8)×D59, C2×#21432901, #29452772, … |
| maximal quotient of | #28558100, #28558269, #28558295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13315);