Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#390 ⋊ C2 |
| Sylow | C59 ⋊ #2006 |
406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,h^b=h^58,e^c=eg,h^c=h^58838 conjugacy classes — view the full character table.
| maximal subgroup of | #28476213, #28476215, #28500752, … |
| maximal normal subgroup of | #28476213, #28476215, #28500752, … |
| maximal quotient of | #28488996, #28489003, #28489010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5551);