Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C19 · Schur multiplier (H2) = C33 |
| direct product | C19×#10624666 |
| 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 | |
236 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)(3,9,14)(4,8,15)(6,16,12)(7,19,13)(10,21,24)(11,18,26)(17,27,23)(20,25,22)(28,29,32,31,35,42,40,34,46)(30,36,47,39,33,43,38,45,41)(37,44,51,49,53,54,50,48,52)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(1,3,10,4,12,22,13,11,23)(2,6,17,8,18,21,7,9,20)(5,14,24,15,16,25,19,26,27)(28,30,37)(29,33,44)(31,39,49)(32,41,51)(34,36,48)(35,45,53)(38,50,40)(42,47,54)(43,52,46);(2,7,8)(3,11,12)(5,15,19)(6,18,9)(10,22,23)(24,27,25)(29,34,35)(32,42,46)(33,36,45)(41,47,43)(44,48,53)(51,54,52)779 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 226);