Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C19 · Schur multiplier (H2) = C32 |
| direct product | C19×#10624649 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C19 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C19 |
| prime radical | C33×C19 | C33 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C19 ◁ C32×C9×C19 ◁ G | |
178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 4617 |
A minimal faithful permutation representation — 3 generators on 73 points:
(1,2,5)(3,7,12)(4,6,13)(8,17,11)(9,14,21)(10,16,22)(15,24,18)(19,23,26)(20,25,27)(28,29,32,31,34,41,39,45,51)(30,35,46,38,33,42,37,44,40)(36,43,50,48,53,54,49,47,52)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(2,6,8)(3,9,18)(7,15,14)(10,20,19)(12,21,24)(22,27,26)(28,30,36,31,38,48,39,37,49)(29,33,43,34,44,53,45,35,47)(32,40,50,41,46,54,51,42,52);(1,3,10,4,9,19,11,18,20)(2,7,16,6,14,23,8,15,25)(5,12,22,13,21,26,17,24,27)1083 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 209);