Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D4×#11745672 |
| Sylow | C59 ⋊ D4×Q16 |
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
760 conjugacy classes — view the full character table.
| maximal subgroup of | #28578119, #28578122, #28578127, … |
| maximal normal subgroup of | #28578119, #28578122, #28578127, … |
| maximal quotient of | #28578870, #28578876, #28578885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16258);