Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#428 ⋊ C2 |
| Sylow | C59 ⋊ #3351 |
348 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^58,c^b=cg,d^b=de,f^c=fg,h^d=h^58667 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3351, C2×#21436657, #29467450, … |
| maximal normal subgroup of | D59×#3351, C2×#21436657, #29467450, … |
| maximal quotient of | #28605098, #28605119, #28606421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17071);