Finite Group DatabasebetaFinite Group Databasebeta| order | 10406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊D473 |
| unambiguous semidirect product | C43⋊(C11⋊D11) |
| Fitting, socle, derived, Hall | C112×C43 ⋊ C2 |
| Sylow | C112 ⋊ D43 |
| Sylow | C43 ⋊ C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C43 | C2 |
| LCS | G ▷ C112×C43 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,11^2,43|b^a=b^10,c^a=c^10,d^a=d^422603 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D473, D43×C11⋊D11, C2×C11⋊D473, … |
| maximal normal subgroup of | D11×D473, D43×C11⋊D11, C2×C11⋊D473, … |
| maximal quotient of | C11⋊Dic473, C2×C11⋊D473, C3×C11⋊D473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10406, 6);