Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16837783 |
| Fitting | C22×SD16×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#495 |
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 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.
856 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16837783, #28597130, #28597167, … |
| maximal normal subgroup of | C4×#16837783, #28597130, #28597167, … |
| maximal quotient of | C2×#21423686, C2×#21423691, C2×#21423695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14928);