Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C43 · Schur multiplier (H2) = C34 |
| direct product | C43×#10624899 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C43 | C34 |
| commutator, Frattini, cosocle | C32 | C34×C43 |
| prime radical | C34×C43 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C43 ◁ G | |
740 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 3483 |
A minimal faithful permutation representation — 4 generators on 79 points:
(1,2,4,3,6,8,7,5,9)(10,11,14,13,16,23,21,27,34)(12,17,28,20,26,22,19,15,24)(18,30,35,31,25,36,32,29,33)(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);(10,12,18,13,20,31,21,19,32)(11,15,25,16,17,29,27,26,30)(14,22,33,23,24,35,34,28,36);(2,5,6)(4,8,9);(12,19,20)(15,26,17)(18,31,32)(22,28,24)(25,29,30)(33,35,36)5203 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 459);