Finite Group DatabasebetaFinite Group Databasebeta| order | 8646 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C131 · Schur multiplier (H2) = C1 |
| direct product | C3×D11×C131 |
| unambiguous semidirect product | C11⋊(C2×C3×C131) |
| Fitting, socle, Hall | C3×C11×C131 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C3×C131 |
| Hall | C11×C131 ⋊ C2×C3 |
| Hall | C3×C11 ⋊ C2×C131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C131 | D11 |
| commutator, hypocenter | C11 | C2×C3×C131 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C131 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C3×C131 | |
16 conjugacy classes of subgroups.
2751 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×D131, D3×D11×C131, D11×D393, … |
| maximal normal subgroup of | C3×D11×D131, D3×D11×C131, D11×D393, … |
| maximal quotient of | C3×Dic11×C131, C2×C3×D11×C131, C9×D11×C131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8646, 3);