Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C92×C43 · Schur multiplier (H2) = C32 |
| direct product | C43×#10624472 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C43 | C9⋊C9 |
| commutator | C9 | C92×C43 |
| Frattini, cosocle | C32×C9 | C32×C43 |
| prime radical | C33×C43 | 3−1+2 |
| LCS | G ▷ C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C43 ◁ C32×C9×C43 ◁ G | |
170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 3483 |
A minimal faithful permutation representation — 2 generators on 79 points:
(1,2,4)(3,6,8)(5,9,7)(11,15,18,17,26,25,19,27,32)(12,20,33)(13,21,22)(16,28,34,29,30,35,31,36,24)(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);(2,5,6)(4,8,9)(10,11,16,13,18,30,20,27,34,14,19,29,22,32,36,33,26,35,23,17,31,21,25,28,12,15,24)4515 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 32);