Finite Group DatabasebetaFinite Group Databasebeta| order | 19140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic4785 |
| unambiguous semidirect product | C3⋊Dic1595 |
| unambiguous semidirect product | C11⋊Dic435 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D4785 |
| commutator, hypocenter | C3×C5×C11×C29 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C11×C29 | C2 |
| LCS | G ▷ C3×C5×C11×C29 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 52 |
| transitive degree | μt(G) = 19140 |
A minimal faithful permutation representation — 2 generators on 52 points:
(1,2)(3,4)(5,6,7)(8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52);(1,3,2,4)(6,7)(9,12)(10,11)(14,23)(15,22)(16,21)(17,20)(18,19)(25,52)(26,51)(27,50)(28,49)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,39)Polycyclic presentation:
2,3,5,11,29,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^10,e^a=e^284788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic9570, Dic14355 |
| maximal normal subgroup of | Dic9570 |
| maximal quotient of | Dic14355 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19140, 17);