Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16837785 |
| 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 | #28506909, #28506914, #28506953, … |
| maximal normal subgroup of | #28506909, #28506914, #28506953, … |
| maximal quotient of | C2×#21423685, C2×#21423694, C2×#21423696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14930);