Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#16837197 |
| Sylow | C59 ⋊ C2×#354 |
284 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
838 conjugacy classes — view the full character table.
| maximal subgroup of | #28476416, #28476417, #28476440, … |
| maximal normal subgroup of | #28476416, #28476417, #28476440, … |
| maximal quotient of | C2×#21422030, C2×#21422040, #28497967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6171);