Finite Group DatabasebetaFinite Group Databasebeta| order | 21420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic5355 |
| unambiguous semidirect product | C7⋊Dic765 |
| unambiguous semidirect product | C9⋊Dic595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5355 |
| commutator, hypocenter | C5×C7×C9×C17 | C4 |
| Frattini | C2×C3 | D1785 |
| Fitting, cosocle | C2×C5×C7×C9×C17 | C2 |
| socle, prime radical | C2×C3×C5×C7×C17 | D3 |
| LCS | G ▷ C5×C7×C9×C17 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 21420 |
A minimal faithful permutation representation — 2 generators on 42 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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,18)(16,17)(20,25)(21,24)(22,23)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)Polycyclic presentation:
2,3,5,7,17,2,3|a^2=f,b^3=g^2,b^a=b^2g,c^a=c^4,d^a=d^6,e^a=e^16,g^a=g^25358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic10710, Dic16065 |
| maximal normal subgroup of | Dic10710 |
| maximal quotient of | Dic16065 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21420, 17);