Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#470 ⋊ C2 |
| Sylow | C59 ⋊ #3054 |
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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^2=e,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^58,c^b=cg,h^b=h^58,h^d=h^58496 conjugacy classes — view the full character table.
| maximal subgroup of | #28498838, #28498851, #28742586, … |
| maximal normal subgroup of | #28498838, #28498851, #28742586, … |
| maximal quotient of | #28571205, #28571233, #28571275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14121);