Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C59 ⋊ #1363 |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=e,c^2=fg,d^2=ef,f^2=g,b^a=bc,c^a=ce,h^a=h^58,c^b=cf,d^b=def,f^b=fg,h^b=h^58841 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1363, C2×#21422149, #28499953, … |
| maximal normal subgroup of | D59×#1363, C2×#21422149, #28499953, … |
| maximal quotient of | #28475478, #28475481, #28475879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2563);