Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#15689255 |
| Fitting | C22×D8×C47 ⋊ C2 |
| Sylow | C47 ⋊ C2×#447 |
1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
682 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#15689255, #26221850, #26221917, … |
| maximal normal subgroup of | C4×#15689255, #26221850, #26221917, … |
| maximal quotient of | C2×#20242304, C2×#20242372, C2×#20242321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13684);