Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C19 · Schur multiplier (H2) = C34 |
| direct product | C19×#10624877 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C19 | C33 |
| commutator, Frattini, cosocle | C32 | C34×C19 |
| socle | C32×C19 | C34 |
| prime radical | C3×C19×H(3,𝔽3) | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C19 ◁ G | |
662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 4617 |
A minimal faithful permutation representation — 4 generators on 73 points:
(1,2,5)(3,7,13)(4,8,12)(6,14,11)(9,16,21)(10,17,20)(15,22,19)(18,24,26)(23,27,25)(28,29,32)(30,33,39)(31,35,40)(34,44,38)(36,41,47)(37,43,48)(42,51,46)(45,50,53)(49,54,52)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(2,6,8)(5,12,14)(7,15,17)(13,20,22)(16,23,24)(21,26,27)(28,30,36,31,37,45,38,46,52)(29,33,41,35,43,50,34,42,49)(32,39,47,40,48,53,44,51,54);(29,34,35)(32,40,44)(33,42,43)(39,48,51)(41,49,50)(47,53,54);(1,3,9,4,10,18,11,19,25)(2,7,16,8,17,24,6,15,23)(5,13,21,12,20,26,14,22,27)2907 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 437);