Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#16837544 |
| Fitting | C22×D8×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#449 |
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
850 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16837544, #28594307, #28594372, … |
| maximal normal subgroup of | C4×#16837544, #28594307, #28594372, … |
| maximal quotient of | C2×#21423022, C2×#21423090, C2×#21423039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13708);