Finite Group DatabasebetaFinite Group Databasebeta| order | 16767 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×#10624496 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C23 | #6862 |
| commutator, Frattini, cosocle | C34 | C32×C23 |
| prime radical | C34×C23 | C32 |
| LCS | G ▷ C34 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C23 ◁ C33×C23 ◁ C34×C23 ◁ G | |
106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 621 |
A minimal faithful permutation representation — 2 generators on 50 points:
(1,2,5)(3,9,14,11,6,16,12,18,24)(4,7,15)(8,19,13)(10,17,25,22,20,23,21,26,27)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50);(1,3,10)(2,6,17,8,9,20,7,18,26)(4,11,21)(5,14,23,15,16,25,19,24,27)(12,22,13)943 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16767, 56);