Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#102×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2012 |
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^58,c^b=cf,d^b=dg,e^b=eg,h^b=h^58,d^c=dg,e^c=eg844 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2012, C2×#21425175, #28615761, … |
| maximal normal subgroup of | D59×#2012, C2×#21425175, #28615761, … |
| maximal quotient of | #28489117, #28489125, #28489139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5589);