Finite Group DatabasebetaFinite Group Databasebeta| order | 10406 |
| automorphism | Aut(G) order 24037860 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5203 |
| unambiguous semidirect product | C43⋊D121 |
| unambiguous semidirect product | C121⋊D43 |
| Fitting, derived, Hall | C43×C121 ⋊ C2 |
| Sylow | C121 ⋊ D43 |
| Sylow | C43 ⋊ D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C43×C121 | C2 |
| Frattini | C11 | D473 |
| socle | C11×C43 | D11 |
| LCS | G ▷ C43×C121 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,43,11|b^11=d^10,b^a=b^10d,c^a=c^42,d^a=d^102603 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D121, C2×D5203, C3×D5203, … |
| maximal normal subgroup of | D43×D121, C2×D5203, C3×D5203, … |
| maximal quotient of | Dic5203, C2×D5203, C3×D5203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10406, 4);