Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | H(3,ℤ/4)×D47 |
| Fitting | C47×H(3,ℤ/4) ⋊ C2 |
| Sylow | C47 ⋊ C2×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C42×D47 |
| commutator | C4×C47 | C2×C42 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×H(3,ℤ/4) | C2 |
| socle | C2×C47 | C2×#95 |
| hypercenter | H(3,ℤ/4) | D47 |
| hypocenter | C47 | C2×H(3,ℤ/4) |
| LCS | G ▷ C4×C47 ▷ C47 | |
| UCS | C1 ◁ C4 ◁ H(3,ℤ/4) | |
404 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
550 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1339, D47×#1340, #26126425, … |
| maximal normal subgroup of | D47×#1339, D47×#1340, #26126425, … |
| maximal quotient of | D47×#1274, #26105675, #26105678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4209);