Finite Group DatabasebetaFinite Group Databasebeta| order | 20646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#20293717 |
| Fitting, socle, derived | C3×C31×C37 ⋊ C2×C3 |
| Hall | C3×#16812216 ⋊ C2 |
| Hall | C31×C37 ⋊ C3×D3 |
| Sylow | C37 ⋊ C3⋊(D31⋊C3) |
| Sylow | C31 ⋊ C3⋊(D37⋊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:
(2,6,7,3,4,8)(5,14,15,9,10,23)(11,26,27,17,18,34)(12,25,21,19,16,13)(20,36,37,29,28,32)(22,24,35,31,30,33)(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);(1,2,5,11,18,28,33,34,31,21,7,6,12,20,30,10,16,23,32,37,15,25,14,24,29,19,4,8,13,22,27,35,36,26,17,9,3)(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,e^a=e^36,d^b=d^5,e^b=e^26582 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20646, 57);