Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1407 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=g,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^58,c^b=cf,d^b=defg,e^b=eg,d^c=dfg,e^d=eg478 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1407, C2×#21422256, #28508976, … |
| maximal normal subgroup of | D59×#1407, C2×#21422256, #28508976, … |
| maximal quotient of | #28476070, #28476108, #28476199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2670);