Finite Group DatabasebetaFinite Group Databasebeta| order | 10764 |
| automorphism | Aut(G) order 8525088 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2691 |
| unambiguous semidirect product | C9⋊Dic299 |
| unambiguous semidirect product | C23⋊Dic117 |
| derived, Hall | C9×C13×C23 ⋊ C4 |
| Hall | C13×C23 ⋊ Dic9 |
| Hall | C9×C23 ⋊ Dic13 |
| Hall | C9×C13 ⋊ Dic23 |
| Sylow | C23 ⋊ Dic117 |
| Sylow | C13 ⋊ Dic207 |
| Sylow | C9 ⋊ Dic299 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2691 |
| commutator, hypocenter | C9×C13×C23 | C4 |
| Frattini | C2×C3 | D897 |
| Fitting, cosocle | C2×C9×C13×C23 | C2 |
| socle, prime radical | C2×C3×C13×C23 | D3 |
| LCS | G ▷ C9×C13×C23 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,23,2,3|a^2=e,b^3=f^2,b^a=b^2f,c^a=c^12,d^a=d^22,f^a=f^22694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic5382, Dic8073, Dic13455 |
| maximal normal subgroup of | Dic5382 |
| maximal quotient of | Dic8073, Dic13455 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10764, 12);