Finite Group DatabasebetaFinite Group Databasebeta| order | 1386 |
| isoclinism | isoclinic class of D231 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D231 |
| unambiguous semidirect product | C3⋊(C3×D77) |
| unambiguous semidirect product | C11⋊(C3×D21) |
| Fitting, socle, Hall | C32×C7×C11 ⋊ C2 |
| derived | C3×C7×C11 ⋊ C2×C3 |
| Hall | C32×C11 ⋊ D7 |
| Hall | C7×C11 ⋊ C3×D3 |
| Hall | C32×C7 ⋊ D11 |
| Sylow | C11 ⋊ C3×D21 |
| Sylow | C32 ⋊ D77 |
| Sylow | C7 ⋊ C3×D33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D231 |
| commutator, cosocle, hypocenter | C3×C7×C11 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C11 | C2 |
| LCS | G ▷ C3×C7×C11 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 462 |
351 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×D21, C3×D7×D33, C3×D3×D77, … |
| maximal normal subgroup of | C3×D11×D21, C3×D7×D33, C3×D3×D77, … |
| maximal quotient of | C3×Dic231, C2×C3×D231, C3×D2541, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1386, 27);