Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C27×C43 · Schur multiplier (H2) = C33 |
| direct product | C43×#10624463 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C9×C43 | C32 |
| commutator | C3 | C9×C27×C43 |
| Frattini, cosocle | C32×C9 | C32×C43 |
| socle, prime radical | C33×C43 | C3×C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C9×C43 ◁ G | |
230 conjugacy classes of subgroups.
| minimal degree | μ(G) = 88 |
| transitive degree | μt(G) = 31347 |
A minimal faithful permutation representation — 2 generators on 88 points:
(1,2,4)(3,6,8)(5,9,7)(19,20,23,21,24,29,26,31,36,22,25,30,27,32,37,34,39,42,28,33,38,35,40,43,41,44,45)(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);(2,5,6)(4,8,9)(10,11,13,12,14,16,15,17,18)12771 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 23);