Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C19 · Schur multiplier (H2) = C33 |
| direct product | C19×#10624838 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C19 | C3×#732 |
| commutator, Frattini, cosocle | C3×C9 | C33×C19 |
| prime radical | C3×C19×#732 | C3 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C19 ◁ C33×C19 ◁ C32×C9×C19 ◁ G | |
198 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)(3,11,31)(4,16,21)(5,10,22)(7,23,42)(8,27,18)(9,30,19)(12,36,67)(13,33,54)(14,41,20)(15,35,63)(17,45,51)(24,56,72)(25,53,73)(26,55,74)(28,61,75)(29,60,47)(32,48,71)(34,50,43)(37,68,78)(38,57,62)(39,69,52)(40,66,49)(44,59,46)(58,79,70)(64,76,80)(65,77,81)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100);(1,3,12)(2,7,24,10,26,57,9,25,58)(4,14,38)(5,15,37)(6,20,48,30,49,77,22,50,76)(8,11,32,29,35,64,16,33,65)(13,39,19)(17,42,71)(18,43,70)(21,23,52,60,53,78,27,55,67)(28,34,36,45,66,68,44,41,69)(31,62,51,54,56,61,63,79,59)(40,72,47)(46,74,80)(73,81,75);(3,13,15)(7,25,26)(11,33,35)(12,37,39)(14,40,43)(20,49,50)(23,53,55)(24,57,58)(31,54,63)(32,64,65)(34,41,66)(36,68,69)(38,70,72)(42,73,74)(48,76,77)(52,67,78)(56,62,79)(71,80,81)1083 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 398);