Finite Group DatabasebetaFinite Group Databasebeta| order | 2046 |
| isoclinism | isoclinic class of C11⋊(D31⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D31⋊C3) |
| unambiguous semidirect product | (C31⋊C3)⋊D11 |
| unambiguous semidirect product | D341⋊C3 |
| Fitting, socle, derived, Hall | C11×C31 ⋊ C2×C3 |
| Hall | C11×C31⋊C3 ⋊ C2 |
| Hall | D341 ⋊ C3 |
| Hall | C31⋊C3 ⋊ D11 |
| Sylow | C31 ⋊ C3×D11 |
| Sylow | C11 ⋊ D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C31 | C2×C3 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 341 |
Polycyclic presentation:
2,3,11,31|c^a=c^10,d^a=d^30,d^b=d^2576 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2046, 12);