Finite Group DatabasebetaFinite Group Databasebeta| order | 10188 |
| automorphism | Aut(G) order 8619048 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2547 |
| unambiguous semidirect product | C9⋊Dic283 |
| unambiguous semidirect product | C283⋊Dic9 |
| derived, Hall | C9×C283 ⋊ C4 |
| Sylow | C283 ⋊ Dic9 |
| Sylow | C9 ⋊ Dic283 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2547 |
| commutator, hypocenter | C9×C283 | C4 |
| Frattini | C2×C3 | D849 |
| Fitting, cosocle | C2×C9×C283 | C2 |
| socle, prime radical | C2×C3×C283 | D3 |
| LCS | G ▷ C9×C283 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,283,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^282,e^a=e^22550 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic5094, Dic7641, Dic12735 |
| maximal normal subgroup of | Dic5094 |
| maximal quotient of | Dic7641, Dic12735 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10188, 6);