Finite Group DatabasebetaFinite Group Databasebeta| order | 20130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20269514⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C61 | C2×C3×C5 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 72 |
| transitive degree | μt(G) = 671 |
A minimal faithful permutation representation — 2 generators on 72 points:
(2,18,40,17,47,11,5,38,48,37,4,25,12,36,19,3,10,45,24,26,9,8,23,56,34,7,22,20,41,39)(6,42,49,46,61,54,16,31,50,44,15,13,35,53,52,14,21,30,55,57,33,29,43,51,59,32,28,27,58,60)(63,64,66,69,68)(65,67,71,72,70);(1,2,6,17,18,25,46,59,42,5,13,31,47,9,7,19,40,51,16,36,12,27,48,58,61,23,33,37,32,30,52,60,49,15,34,54,38,57,53,56,35,20,41,29,50,45,39,4,11,26,43,28,8,21,44,55,22,10,24,14,3)(62,63,65,68,64,66,70,72,67,69,71)Polycyclic presentation:
2,3,5,11,61|e^a=e^60,e^b=e^47,d^c=d^4,e^c=e^964 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20130, 81);