Finite Group DatabasebetaFinite Group Databasebeta| order | 16767 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×#10624487 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C23 | #6857 |
| commutator, Frattini, cosocle | C32×C9 | C32×C23 |
| prime radical | C33×C23 | H(3,𝔽3) |
| LCS | G ▷ C32×C9 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C23 ◁ C33×C23 ◁ C32×C9×C23 ◁ G | |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 104 |
| transitive degree | μt(G) = 1863 |
A minimal faithful permutation representation — 2 generators on 104 points:
(1,2,6,19,9,31,5,10,22)(3,11,32,15,27,55,14,35,66)(4,8,21,48,29,64,18,30,53)(7,23,46,26,57,45,25,56,41)(12,36,69)(13,39,50,42,34,20,16,44,51)(17,28,52,76,62,81,47,63,78)(24,58,37)(33,67,75)(38,70,79)(40,59,65)(43,72,54)(49,71,61)(60,80,74)(68,77,73)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104);(1,3,12,5,15,38,19,14,43)(2,7,24,10,26,59,9,25,60)(4,16,37,18,13,40,48,42,74)(6,20,49,22,51,77,31,50,67)(8,27,61,30,35,68,29,11,33)(17,46,71,47,45,73,76,41,75)(21,23,54,53,57,69,64,56,79)(28,39,72,63,34,36,62,44,70)(32,65,52,55,80,78,66,58,81)943 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16767, 47);