Finite Group DatabasebetaFinite Group Databasebeta| order | 17739 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C92×C73 · Schur multiplier (H2) = C3 |
| direct product | C73×#6864 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C73 | C32 |
| commutator | C3 | C92×C73 |
| Frattini, cosocle | C3×C9 | C32×C73 |
| socle, prime radical | C32×C73 | C3×C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C73 ◁ G | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 17739 |
A minimal faithful permutation representation — 2 generators on 109 points:
(10,11,14,12,16,22,18,25,30,13,17,21,19,26,29,27,33,35,20,15,23,28,24,31,34,32,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(1,2,4,3,5,7,6,8,9)(11,15,17)(14,21,23)(16,24,26)(22,29,31)(25,32,33)(30,35,36)7227 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17739, 11);