Finite Group DatabasebetaFinite Group Databasebeta| order | 7002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1167 |
| unambiguous semidirect product | C3⋊(C3×D389) |
| unambiguous semidirect product | C389⋊(C3×D3) |
| Fitting, socle, Hall | C32×C389 ⋊ C2 |
| derived | C3×C389 ⋊ C2×C3 |
| Sylow | C389 ⋊ C3×D3 |
| Sylow | C32 ⋊ D389 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1167 |
| commutator, hypocenter | C3×C389 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C389 | C2 |
| LCS | G ▷ C3×C389 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
1755 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×D389, D3×D1167, (C3⋊D3)⋊D389, … |
| maximal normal subgroup of | C3×D3×D389, D3×D1167, (C3⋊D3)⋊D389, … |
| maximal quotient of | C3×Dic1167, C2×C3×D1167, C3×C5×D1167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7002, 8);