Finite Group DatabasebetaFinite Group Databasebeta| order | 20646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#20293713 |
| Fitting, socle, derived | C3×C31×C37 ⋊ C2×C3 |
| Hall | C3×#16812216 ⋊ C2 |
| Hall | C31×C37 ⋊ C3×D3 |
| Sylow | C37 ⋊ C3⋊(D31⋊C3) |
| Sylow | C31 ⋊ D3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C31×C37 | C2×C3 |
| LCS | G ▷ C3×C31×C37 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3441 |
A minimal faithful permutation representation — 2 generators on 71 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,21)(11,16,18)(13,19,15)(17,24,28)(20,26,25)(22,29,23)(27,32,33)(30,34,31)(35,37,36)(39,43,44,40,41,45)(42,51,52,46,47,59)(48,62,63,54,55,67)(49,61,57,56,53,50)(58,60,68,64,65,66)(70,71);(1,2,4,8,14,22,30,35,34,19,5,9,15,23,24,7,13,20,27,29,12,18,25,31,32,16,3,6,11,17,21,28,33,36,37,26,10)(38,39,42,48,56,41,45,50,58,65,47,53,59,63,68,55,62,66,67,52,61,51,60,64,57,44,43,49,54,46,40)(69,70,71)Polycyclic presentation:
2,3^2,31,37|c^a=c^2,d^a=d^30,d^b=d^5,e^b=e^26600 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20646, 59);