Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C59×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C59 ⋊ #2122 |
266 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 55 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,c^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,e^b=ef,h^c=h^58,e^d=eg400 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2122, C2×#21425744, #28741428, … |
| maximal normal subgroup of | D59×#2122, C2×#21425744, #28741428, … |
| maximal quotient of | #28497780, #28497868, #28497946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6158);