Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C59×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C59 ⋊ #2199 |
270 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 41 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^a=bd,c^a=ce,f^a=fg,h^a=h^58,c^b=cg,e^b=efg,d^c=df,h^c=h^58,e^d=eg394 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2199, C2×#21426098, #28742737, … |
| maximal normal subgroup of | D59×#2199, C2×#21426098, #28742737, … |
| maximal quotient of | #28500737, #28500738, #28500777, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6512);