Finite Group DatabasebetaFinite Group Databasebeta| order | 7002 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C389 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C389 |
| unambiguous semidirect product | C3⋊(D3×C389) |
| Fitting, socle, Hall | C32×C389 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C389 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C389 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C389 |
| Frattini | C1 | G |
| Fitting, socle | C32×C389 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C389 | |
24 conjugacy classes of subgroups.
2334 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×D389, D32×C389, (C3⋊D3)⋊D389, … |
| maximal normal subgroup of | C3⋊D3×D389, D32×C389, (C3⋊D3)⋊D389, … |
| maximal quotient of | C3⋊Dic3×C389, C2×C3⋊D3×C389, C5×C3⋊D3×C389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7002, 9);