Finite Group DatabasebetaFinite Group Databasebeta| order | 8646 |
| isoclinism | isoclinic class of D131 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×D131 |
| unambiguous semidirect product | C131⋊(C2×C3×C11) |
| Fitting, socle, Hall | C3×C11×C131 ⋊ C2 |
| derived, Sylow | C131 ⋊ C2×C3×C11 |
| Hall | C11×C131 ⋊ C2×C3 |
| Hall | C3×C131 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | D131 |
| commutator, hypocenter | C131 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C131 | C2 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C3×C11 | |
16 conjugacy classes of subgroups.
2211 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×D131, D3×C11×D131, D33×D131, … |
| maximal normal subgroup of | C3×D11×D131, D3×C11×D131, D33×D131, … |
| maximal quotient of | C3×C11×Dic131, C2×C3×C11×D131, C9×C11×D131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8646, 2);