Finite Group DatabasebetaFinite Group Databasebeta| order | 1914 |
| isoclinism | isoclinic class of D319 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D319 |
| unambiguous semidirect product | C11⋊(C3×D29) |
| unambiguous semidirect product | C29⋊(C3×D11) |
| Fitting, socle, Hall | C3×C11×C29 ⋊ C2 |
| derived, Hall | C11×C29 ⋊ C2×C3 |
| Hall | C3×C29 ⋊ D11 |
| Hall | C3×C11 ⋊ D29 |
| Sylow | C29 ⋊ C3×D11 |
| Sylow | C11 ⋊ C3×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D319 |
| commutator, cosocle, hypocenter | C11×C29 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C29 | C2 |
| LCS | G ▷ C11×C29 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 957 |
483 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×D29, D3×D319, D33⋊D29, … |
| maximal normal subgroup of | C3×D11×D29, D3×D319, D33⋊D29, … |
| maximal quotient of | C3×Dic319, C2×C3×D319, C3×C7×D319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1914, 3);