Finite Group DatabasebetaFinite Group Databasebeta| order | 16767 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C92×C23 · Schur multiplier (H2) = C32 |
| direct product | C23×#10624465 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C23 | C92 |
| commutator | C9 | C92×C23 |
| Frattini, cosocle | C32×C9 | C32×C23 |
| socle | C3×C23 | #6855 |
| prime radical | C33×C23 | 3−1+2 |
| LCS | G ▷ C9 ▷ C1 | |
| UCS | C1 ◁ C9×C23 ◁ G | |
156 conjugacy classes of subgroups.
| minimal degree | μ(G) = 104 |
| transitive degree | μt(G) = 1863 |
A minimal faithful permutation representation — 2 generators on 104 points:
(1,2,7,5,10,24,18,32,56,6,11,26,20,34,58,48,66,55,21,35,25,17,31,54,4,9,23)(3,12,36,15,38,60,47,68,53,16,39,57,19,8,27,14,29,52,44,65,69,50,30,61,45,33,22)(13,40,73,42,71,51,41,72,78,43,67,59,46,76,79,74,28,62,75,63,81,49,37,70,77,64,80)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104);(1,3,13)(2,8,28,11,30,64,35,38,72)(4,14,41)(5,19,49)(6,16,43)(7,22,51,25,52,70,26,53,79)(9,12,37,32,39,71,66,65,76)(10,33,67,34,68,63,31,29,40)(15,46,17)(18,45,74)(20,50,42)(21,44,75)(23,27,59,55,60,73,56,61,81)(24,57,80,54,36,62,58,69,78)(47,77,48)2415 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16767, 25);