Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C59×#357 ⋊ C2 |
| Sylow | C59 ⋊ #2189 |
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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,c^2=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^58,d^b=df,f^b=fg,h^c=h^58667 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2189, C2×#21426037, #28742462, … |
| maximal normal subgroup of | D59×#2189, C2×#21426037, #28742462, … |
| maximal quotient of | #28500815, #28501159, #28501919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6451);