Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×M32×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2220 |
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|b^2=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^58,c^b=cg1186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#2220, C2×#21426209, #28743154, … |
| maximal normal subgroup of | D59×#2220, C2×#21426209, #28743154, … |
| maximal quotient of | #28502922, #28502973, #28503041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6623);