Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #2000 |
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^58,c^b=cf,d^b=dg844 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2000, C2×#21425099, #28615489, … |
| maximal normal subgroup of | D59×#2000, C2×#21425099, #28615489, … |
| maximal quotient of | #28488897, #28488904, #28488925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5513);