Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1838 |
180 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=f,b^2=e,c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^58,c^b=cg1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475859, #28483088, #28483089, … |
| maximal normal subgroup of | #28475859, #28483088, #28483089, … |
| maximal quotient of | #28482356, #28482360, #28482363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4651);