Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#392 ⋊ C2 |
| Sylow | C59 ⋊ #1595 |
368 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 368 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|d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=eg,h^b=h^58,d^c=dg661 conjugacy classes — view the full character table.
| maximal subgroup of | #28500718, #28500719, #28500729, … |
| maximal normal subgroup of | #28500718, #28500719, #28500729, … |
| maximal quotient of | #28477386, #28477389, #28477396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3427);