Finite Group DatabasebetaFinite Group Databasebeta| order | 9468 |
| automorphism | Aut(G) order 7441848 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2367 |
| unambiguous semidirect product | C9⋊Dic263 |
| unambiguous semidirect product | C263⋊Dic9 |
| derived, Hall | C9×C263 ⋊ C4 |
| Sylow | C263 ⋊ Dic9 |
| Sylow | C9 ⋊ Dic263 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2367 |
| commutator, hypocenter | C9×C263 | C4 |
| Frattini | C2×C3 | D789 |
| Fitting | C2×C9×C263 | C2 |
| socle | C2×C3×C263 | D3 |
| LCS | G ▷ C9×C263 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,263,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^262,e^a=e^22370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic4734, Dic7101 |
| maximal normal subgroup of | Dic4734 |
| maximal quotient of | Dic7101 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9468, 4);