Finite Group DatabasebetaFinite Group Databasebeta| order | 11754 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1959 |
| unambiguous semidirect product | C3⋊(C3×D653) |
| unambiguous semidirect product | C653⋊(C3×D3) |
| Fitting, socle, Hall | C32×C653 ⋊ C2 |
| derived | C3×C653 ⋊ C2×C3 |
| Sylow | C653 ⋊ C3×D3 |
| Sylow | C32 ⋊ D653 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1959 |
| commutator, cosocle, hypocenter | C3×C653 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C653 | C2 |
| LCS | G ▷ C3×C653 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
2943 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×D653, D3×D1959, (C3⋊D3)⋊D653, … |
| maximal normal subgroup of | C3×D3×D653, D3×D1959, (C3⋊D3)⋊D653, … |
| maximal quotient of | C3×Dic1959, C2×C3×D1959 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11754, 8);