Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C59×#376 ⋊ C2 |
| Sylow | C59 ⋊ #1759 |
320 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=e,b^2=f,c^2=e,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^58,c^b=cg1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28480540, #28480542, #28480547, … |
| maximal normal subgroup of | #28480540, #28480542, #28480547, … |
| maximal quotient of | #28479292, #28479297, #28479312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4321);