Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#16837777 |
| Fitting | C22×D8×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#493 |
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #28506901, #28506919, #28506947, … |
| maximal normal subgroup of | #28506901, #28506919, #28506947, … |
| maximal quotient of | C2×#21423685, C2×#21423687, C2×#21423689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14920);