Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C59×#367 ⋊ C2 |
| Sylow | C59 ⋊ #2219 |
150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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=g,b^2=df,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^58,c^b=cg,h^c=h^58664 conjugacy classes — view the full character table.
| maximal subgroup of | #28509368, #28509655, D59×#2219, … |
| maximal normal subgroup of | #28509368, #28509655, D59×#2219, … |
| maximal quotient of | #28502918, #28502969, #28503037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6619);