Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C19 · Schur multiplier (H2) = C33 |
| direct product | C19×#10624841 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C19 | C3×#732 |
| commutator, Frattini, cosocle | C3×C9 | C33×C19 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C19 ◁ C3×C9×C19 ◁ C32×C9×C19 ◁ G | |
188 conjugacy classes of subgroups.
| minimal degree | μ(G) = 100 |
| transitive degree | μt(G) = 1539 |
A minimal faithful permutation representation — 3 generators on 100 points:
(1,2,7)(3,13,39)(4,9,25)(5,21,26)(6,12,27)(8,28,15)(10,36,19)(11,38,23)(14,44,74)(16,33,24)(17,43,71)(18,32,62)(20,35,58)(22,34,59)(29,63,77)(30,61,49)(31,67,53)(37,69,54)(40,55,48)(41,57,51)(42,56,50)(45,72,80)(46,65,70)(47,66,81)(52,73,79)(60,76,68)(64,78,75)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100);(1,3,14)(2,8,29,12,32,65,11,31,64)(4,18,52)(5,16,46)(6,17,47)(7,24,55,38,61,80,27,57,79)(9,33,68,35,41,44,34,30,66)(10,13,40,37,43,73,21,42,72)(15,48,22)(19,51,75)(20,53,45)(23,50,76)(25,39,70,59,56,63,58,71,78)(26,28,60,69,67,81,36,62,74)(49,77,54);(1,4,19,6,20,54,23,22,5)(2,9,10,12,35,37,11,34,21)(3,15,49,17,18,16,50,53,51)(7,25,36,27,58,69,38,59,26)(8,30,43,32,33,42,31,41,13)(14,45,46,47,48,75,76,52,77)(24,56,67,57,39,28,61,71,62)(29,44,72,65,66,40,64,68,73)(55,78,60,79,63,74,80,70,81)1083 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 401);