Finite Group DatabasebetaFinite Group Databasebeta| order | 9684 |
| automorphism | Aut(G) order 7785936 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2421 |
| unambiguous semidirect product | C9⋊Dic269 |
| derived, Hall | C9×C269 ⋊ C4 |
| Sylow | C269 ⋊ Dic9 |
| Sylow | C9 ⋊ Dic269 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2421 |
| commutator, hypocenter | C9×C269 | C4 |
| Frattini | C2×C3 | D807 |
| Fitting, cosocle | C2×C9×C269 | C2 |
| socle, prime radical | C2×C3×C269 | D3 |
| LCS | G ▷ C9×C269 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,269,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^268,e^a=e^22424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic4842, Dic7263 |
| maximal normal subgroup of | Dic4842 |
| maximal quotient of | Dic7263 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9684, 4);