Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #6878 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C19 · Schur multiplier (H2) = C33 |
| direct product | C3×C19×#6880 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C19 | #732 |
| commutator, Frattini, cosocle | C3×C9 | C33×C19 |
| prime radical | C33×C19 | H(3,𝔽3) |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C19 ◁ C33×C19 ◁ C32×C9×C19 ◁ G | |
224 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1539 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49);(4,5,8,7,11,18,14,23,17)(6,10,15,13,20,16,25,30,27)(9,19,29,21,28,12,22,26,24);(5,9,20,11,21,30,23,22,10)(8,15,26,17,27,28,18,16,19)1995 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 396);