Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C19 · Schur multiplier (H2) = C33 |
| direct product | C19×#10624619 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C19 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C19 |
| prime radical | C34×C19 | C32 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C19 ◁ C34×C19 ◁ G | |
260 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 1539 |
A minimal faithful permutation representation — 3 generators on 73 points:
(1,2,5,4,8,14,12,7,18)(3,9,13,11,6,15,22,17,25)(10,20,23,21,19,24,27,16,26)(28,29,32,39,45,51,31,34,41)(30,35,46,37,44,40,38,33,42)(36,43,50,49,47,52,48,53,54)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(1,3,10,4,11,21,12,22,27)(2,6,16,8,17,20,7,9,19)(5,13,23,14,15,24,18,25,26)(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);(2,7,8)(5,14,18)(6,9,17)(13,15,25)(16,19,20)(23,24,26)1387 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 179);