Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C59×#360 ⋊ C2 |
| Sylow | C59 ⋊ #2190 |
226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|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,e^b=eg,f^b=fg,d^c=dg,h^c=h^58484 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2190, C2×#21426043, #28742586, … |
| maximal normal subgroup of | D59×#2190, C2×#21426043, #28742586, … |
| maximal quotient of | #28500787, #28500792, #28500798, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6457);