Finite Group DatabasebetaFinite Group Databasebeta| order | 20862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#20294356 |
| Fitting, socle, derived | C3×C19×C61 ⋊ C2×C3 |
| Hall | C3×#16812465 ⋊ C2 |
| Hall | C19×C61 ⋊ C3×D3 |
| Sylow | C61 ⋊ C3⋊(D19⋊C3) |
| Sylow | C19 ⋊ C3⋊(D61⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C61 | C2×C3 |
| LCS | G ▷ C3×C19×C61 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3477 |
A minimal faithful permutation representation — 2 generators on 83 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,40)(12,26,22,20,16,13)(19,45,46,30,31,56)(21,43,44,32,29,37)(23,25,42,34,35,38)(33,58,59,48,47,54)(36,41,57,50,49,55)(39,61,60,52,53,51)(63,67,68,64,65,69)(66,75,72,70,71,77)(73,78,80,79,76,74)(82,83);(1,2,5,11,19,31,47,53,55,56,50,34,22,7,6,12,21,33,49,18,29,38,40,54,60,44,15,26,14,25,39,52,35,10,16,24,37,51,59,28,42,43,27,41,48,32,20,4,8,13,23,36,46,57,61,58,45,30,17,9,3)(62,63,66,72,78,75,79,65,69,74,80,68,67,73,71,76,77,70,64)(81,82,83)Polycyclic presentation:
2,3^2,19,61|c^a=c^2,d^a=d^18,e^a=e^60,d^b=d^7,e^b=e^47588 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20862, 58);