Finite Group DatabasebetaFinite Group Databasebeta| order | 10340 |
| automorphism | Aut(G) order 9512800 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2585 |
| unambiguous semidirect product | C11⋊Dic235 |
| unambiguous semidirect product | C47⋊Dic55 |
| derived, Hall | C5×C11×C47 ⋊ C4 |
| Hall | C11×C47 ⋊ Dic5 |
| Hall | C5×C47 ⋊ Dic11 |
| Hall | C5×C11 ⋊ Dic47 |
| Sylow | C47 ⋊ Dic55 |
| Sylow | C11 ⋊ Dic235 |
| Sylow | C5 ⋊ Dic517 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2585 |
| commutator, hypocenter | C5×C11×C47 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C5×C11×C47 | C2 |
| LCS | G ▷ C5×C11×C47 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11,47,2|a^2=e,b^a=b^4,c^a=c^10,d^a=d^462588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2585, Dic7755, Dic5170, … |
| maximal normal subgroup of | C3×Dic2585, Dic5170 |
| maximal quotient of | C3×Dic2585, Dic7755, Dic12925 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10340, 9);