Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C59 ⋊ #1364 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=e,c^2=fg,d^2=efg,f^2=g,b^a=bc,c^a=ce,h^a=h^58,c^b=cf,d^b=def,f^b=fg667 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1364, C2×#21422151, #28499973, … |
| maximal normal subgroup of | D59×#1364, C2×#21422151, #28499973, … |
| maximal quotient of | #28475477, #28475874, #28476340, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2565);