Finite Group DatabasebetaFinite Group Databasebeta| order | 20646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#20293708 |
| Fitting, socle, derived | C3×C31×C37 ⋊ C2×C3 |
| Hall | C3×#16812215 ⋊ C2 |
| Hall | C31×C37 ⋊ C3×D3 |
| Sylow | C37 ⋊ D3×C31⋊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)(5,14,15,9,10,24)(11,27,19,17,18,29)(12,26,22,20,16,13)(21,37,34,31,28,35)(23,25,30,32,33,36)(39,40,42)(41,44,49)(43,47,46)(45,51,58)(48,52,55)(50,56,53)(54,61,64)(57,63,62)(59,65,60)(66,68,67)(70,71);(1,2,5,11,19,30,37,27,31,20,4,8,13,23,34,15,26,14,25,33,10,16,24,35,32,22,7,6,12,21,18,28,36,29,17,9,3)(38,39,41,45,52,40,43,48,54,61,44,50,57,58,64,51,59,66,65,49,55,62,67,68,56,42,46,53,60,63,47)(69,70,71)Polycyclic presentation:
2,3^2,31,37|c^a=c^2,e^a=e^36,d^b=d^5,e^b=e^10597 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20646, 64);