Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×2−1+4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3013 |
712 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,e^b=eg,d^c=dg1018 conjugacy classes — view the full character table.
| maximal subgroup of | #28620148, #28620152, #28620157, … |
| maximal normal subgroup of | #28620148, #28620152, #28620157, … |
| maximal quotient of | #28561904, #28561915, #28561992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13825);