Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#137×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3271 |
488 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=g,c^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=de,e^b=eg,h^c=h^58,e^d=eg667 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3271, C2×#21435675, #29463761, … |
| maximal normal subgroup of | D59×#3271, C2×#21435675, #29463761, … |
| maximal quotient of | #28578135, #28578255, #28578480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16089);