Finite Group DatabasebetaFinite Group Databasebeta| order | 27006 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C643 · Schur multiplier (H2) = C1 |
| direct product | D21×C643 |
| unambiguous semidirect product | C3⋊(D7×C643) |
| unambiguous semidirect product | C7⋊(D3×C643) |
| Fitting, socle, Hall | C3×C7×C643 ⋊ C2 |
| derived, Hall | C3×C7 ⋊ C2×C643 |
| Hall | C7×C643 ⋊ D3 |
| Hall | C3×C643 ⋊ D7 |
| Sylow | C7 ⋊ D3×C643 |
| Sylow | C3 ⋊ D7×C643 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C643 | D21 |
| commutator, cosocle, hypocenter | C3×C7 | C2×C643 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C643 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C643 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13503 |
7716 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27006, 11);