Finite Group DatabasebetaFinite Group Databasebeta| order | 10062 |
| automorphism | Aut(G) order 15213744 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5031 |
| unambiguous semidirect product | C9⋊D559 |
| unambiguous semidirect product | C13⋊D387 |
| unambiguous semidirect product | C43⋊D117 |
| Fitting, derived, Hall | C9×C13×C43 ⋊ C2 |
| Hall | C13×C43 ⋊ D9 |
| Hall | C9×C43 ⋊ D13 |
| Hall | C9×C13 ⋊ D43 |
| Sylow | C43 ⋊ D117 |
| Sylow | C13 ⋊ D387 |
| Sylow | C9 ⋊ D559 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C13×C43 | C2 |
| Frattini | C3 | D1677 |
| socle | C3×C13×C43 | D3 |
| LCS | G ▷ C9×C13×C43 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,43,3|b^3=e^2,b^a=b^2e,c^a=c^12,d^a=d^42,e^a=e^22517 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D117, D13×D387, D9×D559, … |
| maximal normal subgroup of | D43×D117, D13×D387, D9×D559, … |
| maximal quotient of | Dic5031, C2×D5031, D15093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10062, 12);