Finite Group DatabasebetaFinite Group Databasebeta| order | 10782 |
| automorphism | Aut(G) order 19342908 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5391 |
| unambiguous semidirect product | C9⋊D599 |
| unambiguous semidirect product | C599⋊D9 |
| Fitting, derived, Hall | C9×C599 ⋊ C2 |
| Sylow | C599 ⋊ D9 |
| Sylow | C9 ⋊ D599 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C599 | C2 |
| Frattini | C3 | D1797 |
| socle | C3×C599 | D3 |
| LCS | G ▷ C9×C599 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,599,3|b^3=d^2,b^a=b^2d,c^a=c^598,d^a=d^22697 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D599, C2×D5391, D16173, … |
| maximal normal subgroup of | D9×D599, C2×D5391 |
| maximal quotient of | Dic5391, C2×D5391, D16173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10782, 4);