Finite Group DatabasebetaFinite Group Databasebeta| order | 2046 |
| isoclinism | isoclinic class of D31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D31⋊C3 |
| unambiguous semidirect product | D31⋊(C3×C11) |
| unambiguous semidirect product | (C31⋊C3)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D31)⋊C3 |
| Fitting, socle, Hall | C11×C31 ⋊ C2×C3 |
| derived, Sylow | C31 ⋊ C2×C3×C11 |
| Hall | C11×C31⋊C3 ⋊ C2 |
| Hall | C11×D31 ⋊ C3 |
| Hall | C31⋊C3 ⋊ C2×C11 |
| Hall | D31 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C31 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 341 |
A minimal faithful permutation representation — 2 generators on 42 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17,18,14,15,19)(16,25,26,20,21,33)(22,35,36,28,29,41)(23,34,30,31,27,24)(32,42,39,38,37,40);(12,13,16,22,30,18,17,23,32,39,26,34,25,29,37,36,41,42,35,21,27,33,40,38,31,15,19,24,28,20,14)121 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D31⋊C3, C2×C11×D31⋊C3, C7×C11×D31⋊C3, … |
| maximal normal subgroup of | D11×D31⋊C3, C2×C11×D31⋊C3, C7×C11×D31⋊C3, … |
| maximal quotient of | C11×(C31⋊C3)⋊C4, C2×C11×D31⋊C3, C7×C11×D31⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2046, 10);