Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C59 ⋊ #1353 |
116 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=d,b^2=e,c^2=fg,d^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=cf,d^b=defg,h^b=h^58,d^c=dg661 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1353, C2×#21422122, #28498993, … |
| maximal normal subgroup of | D59×#1353, C2×#21422122, #28498993, … |
| maximal quotient of | #28475482, #28475508, #28475812, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2536);