Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C27×C43 · Schur multiplier (H2) = C9 |
| direct product | C43×#10624443 |
| subgroup | G/H | |
|---|---|---|
| center | C92×C43 | C32 |
| commutator | C3 | C9×C27×C43 |
| Frattini, cosocle | C92 | C32×C43 |
| socle, prime radical | C32×C43 | C92 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C92×C43 ◁ G | |
116 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 31347 |
A minimal faithful permutation representation — 2 generators on 97 points:
(1,2,5,3,7,13,9,16,21,4,8,12,10,17,20,18,24,26,11,6,14,19,15,22,25,23,27)(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);(2,6,8)(5,12,14)(7,15,17)(13,20,22)(16,23,24)(21,26,27)(28,29,32,30,33,38,35,40,45,31,34,39,36,41,46,43,48,51,37,42,47,44,49,52,50,53,54)12771 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 3);