Finite Group DatabasebetaFinite Group Databasebeta| order | 20130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20269516⋊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:
(2,16,32,36,55,11,5,19,17,54,4,23,12,24,35,3,10,38,25,44,9,8,21,34,33,7,20,18,39,57)(6,50,47,41,45,46,15,40,61,56,14,58,31,59,60,13,30,26,52,49,29,28,37,48,43,27,42,22,53,51)(63,64,66,69,68)(65,67,71,72,70);(1,2,6,8,19,38,28,52,40,12,26,49,39,9,7,17,35,58,31,16,33,56,20,30,53,55,29,36,27,51,61,48,60,14,25,46,44,59,50,23,43,54,10,22,42,57,34,4,11,24,45,47,18,37,41,15,32,21,5,13,3)(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^5864 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20130, 83);