Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#15689037 |
| Sylow | C47 ⋊ C2×#394 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D47 |
| commutator | C23×C47 | C24 |
| Frattini | C23 | C23×D47 |
| Fitting | C23×D4×C47 | C2 |
| socle | C24×C47 | C23 |
| hypercenter | C23×D4 | D47 |
| hypocenter | C47 | C2×#394 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
1252 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 269 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 | #26111289, #26111294, #26116478, … |
| maximal normal subgroup of | #26111289, #26111294, #26116478, … |
| maximal quotient of | C2×#20241629, C2×#20241631, C2×#20241635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7713);