Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | #364×D47 |
| Fitting | C47×#364 ⋊ C2 |
| Sylow | C47 ⋊ C2×#364 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D47 |
| commutator | C4×C47 | C22×C8 |
| Frattini | C2×C8 | C22×D47 |
| Fitting | C47×#364 | C2 |
| socle | C2×C47 | C2×C4⋊C8 |
| hypercenter | #364 | D47 |
| hypocenter | C47 | C2×#364 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #364 | |
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 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.
700 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1335, #26126063, D47×#1336, … |
| maximal normal subgroup of | D47×#1335, #26126063, D47×#1336, … |
| maximal quotient of | D47×#1367, #26127821, D47×#1370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6271);