Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C35×C19 · Schur multiplier (H2) = C39 |
| direct product | C19×#10624943 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C19 | C34 |
| commutator, Frattini, cosocle | C3 | C35×C19 |
| socle | C3×C19 | C35 |
| prime radical | C19×H(5,𝔽3) | C3 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9×C19 ◁ G | |
5490 conjugacy classes of subgroups.
| minimal degree | μ(G) = 100 |
| transitive degree | μt(G) = 1539 |
A minimal faithful permutation representation — 5 generators on 100 points:
(1,2,6)(3,11,30)(4,9,21)(5,10,20)(7,22,13)(8,26,18)(12,33,46)(14,32,55)(15,24,19)(16,28,45)(17,29,44)(23,48,34)(25,47,37)(27,52,41)(31,42,36)(35,58,68)(38,57,74)(39,50,43)(40,54,67)(49,70,59)(51,69,62)(53,73,64)(56,65,61)(60,76,80)(63,72,66)(71,81,77)(75,79,78)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100);(1,3,12)(2,7,23)(4,14,35)(5,15,34)(6,19,42)(8,24,33)(9,25,49)(10,11,31)(13,36,18)(16,38,60)(17,39,59)(20,22,46)(21,43,65)(26,30,48)(27,50,58)(28,51,71)(29,32,56)(37,61,41)(40,63,77)(44,47,68)(45,66,79)(52,55,70)(53,72,76)(54,57,75)(62,78,64)(67,69,80)(73,74,81);(3,13,15)(7,24,11)(12,34,36)(14,37,39)(19,30,22)(23,31,33)(25,50,32)(35,59,61)(38,62,63)(42,46,48)(43,55,47)(49,56,58)(51,72,57)(60,77,78)(65,68,70)(66,74,69)(71,75,76)(79,80,81);(2,8,10)(6,20,26)(7,24,11)(9,27,29)(19,22,30)(21,44,52)(23,33,31)(25,50,32)(28,53,54)(42,46,48)(43,47,55)(45,67,73)(49,58,56)(51,72,57)(65,68,70)(66,69,74)(71,76,75)(79,80,81);(1,4,16,5,17,40,18,41,64)(2,9,28,10,29,54,8,27,53)(3,14,38,15,39,63,13,37,62)(6,21,45,20,44,67,26,52,73)(7,25,51,11,32,57,24,50,72)(12,35,60,34,59,77,36,61,78)(19,43,66,22,47,69,30,55,74)(23,49,71,31,56,75,33,58,76)(42,65,79,46,68,80,48,70,81)4731 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 503);