Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C19 · Schur multiplier (H2) = C3 |
| direct product | C19×#10624829 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C19 | #6895 |
| commutator, Frattini, cosocle | C3×C9 | C33×C19 |
| prime radical | C33×C19 | 3−1+2 |
| LCS | G ▷ C3×C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C19 ◁ C3×C9×C19 ◁ G | |
128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 100 |
| transitive degree | μt(G) = 1539 |
A minimal faithful permutation representation — 3 generators on 100 points:
(1,2,6,4,10,23,17,31,50,5,11,22,18,34,51,46,30,52,19,9,32,16,33,21,45,8,29)(3,12,20,14,37,49,42,26,59,15,7,24,43,27,55,72,60,75,44,28,54,41,61,48,71,36,62)(13,38,47,39,66,74,68,63,78,40,35,53,69,64,76,81,57,77,70,25,56,67,58,73,80,65,79)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100);(1,3,13,5,15,40,19,44,70)(2,7,25,11,28,38,9,12,35)(4,14,39,18,43,69,16,41,67)(6,20,47,22,24,53,32,54,56)(8,26,57,31,60,65,30,36,63)(10,27,58,34,61,66,33,37,64)(17,42,68,46,72,81,45,71,80)(21,48,73,23,49,74,51,55,76)(29,62,79,50,59,78,52,75,77);(2,8,10,9,30,33,11,31,34)(4,16,18)(6,21,50,22,23,52,32,51,29)(7,26,27,12,36,37,28,60,61)(14,41,43)(17,46,45)(20,48,59,24,49,75,54,55,62)(25,57,58,35,63,64,38,65,66)(39,67,69)(42,72,71)(47,73,78,53,74,77,56,76,79)(68,81,80)1083 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 389);