Finite Group DatabasebetaFinite Group Databasebeta| order | 20130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20269521⋊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:
(2,7,31,21,50,6,4,16,53,38,3,14,9,34,25)(5,26,55,48,45,17,12,46,47,44,11,35,27,61,60)(8,28,20,52,13,15,19,36,30,51,18,33,37,56,29)(10,42,39,54,57,41,24,49,32,40,23,58,43,59,22)(63,67,68,66,71,64,65,72,69,70);(1,2,5,13,30,52,54,27,49,21,39,23,16,6,15,31,14,32,48,29,4,10,25,45,46,7,17,36,57,41,55,58,35,11,9,22,33,42,59,51,12,28,50,43,60,19,37,3,8,20,26,47,56,61,24,44,53,34,38,40,18)(62,63,66,71,65,68,72,67,70,69,64)Polycyclic presentation:
2,3,5,11,61|d^a=d^10,e^b=e^47,d^c=d^4,e^c=e^2061 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20130, 88);