Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#13094057 |
| Fitting | C22×M16×C47 ⋊ C2 |
| Sylow | C47 ⋊ C22×#137 |
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
964 conjugacy classes — view the full character table.
| maximal subgroup of | #26123013, #26123017, #26123027, … |
| maximal normal subgroup of | #26123013, #26123017, #26123027, … |
| maximal quotient of | C22×#15689133, C22×#15689125, C22×#15689165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 19251);