Finite Group DatabasebetaFinite Group Databasebeta| order | 20460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic5115 |
| unambiguous semidirect product | C3⋊Dic1705 |
| unambiguous semidirect product | C11⋊Dic465 |
| unambiguous semidirect product | C31⋊Dic165 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5115 |
| commutator, hypocenter | C3×C5×C11×C31 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C11×C31 | C2 |
| LCS | G ▷ C3×C5×C11×C31 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 20460 |
A minimal faithful permutation representation — 2 generators on 54 points:
(1,2)(3,4)(5,6,7)(8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54);(1,3,2,4)(6,7)(9,12)(10,11)(14,23)(15,22)(16,21)(17,20)(18,19)(25,54)(26,53)(27,52)(28,51)(29,50)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)Polycyclic presentation:
2,3,5,11,31,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^10,e^a=e^305118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic10230, Dic15345 |
| maximal normal subgroup of | Dic10230 |
| maximal quotient of | Dic15345 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20460, 29);