Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#485 ⋊ C2 |
| Sylow | C59 ⋊ #3240 |
328 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=eg,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^58,c^b=ceg,h^b=h^58,f^c=fg577 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3240, C2×#21435340, #29460860, … |
| maximal normal subgroup of | D59×#3240, C2×#21435340, #29460860, … |
| maximal quotient of | #28598229, #28598432, #28599264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15754);