Finite Group DatabasebetaFinite Group Databasebeta| order | 30006 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D5001 |
| unambiguous semidirect product | C3⋊(C3×D1667) |
| unambiguous semidirect product | C1667⋊(C3×D3) |
| Fitting, socle, Hall | C32×C1667 ⋊ C2 |
| derived | C3×C1667 ⋊ C2×C3 |
| Sylow | C1667 ⋊ C3×D3 |
| Sylow | C32 ⋊ D1667 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5001 |
| commutator, cosocle, hypocenter | C3×C1667 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C1667 | C2 |
| LCS | G ▷ C3×C1667 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10002 |
7506 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30006, 8);