Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C43 · Schur multiplier (H2) = C3 |
| direct product | C43×#10624476 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C43 | #6856 |
| commutator, Frattini, cosocle | C34 | C32×C43 |
| prime radical | C34×C43 | C32 |
| LCS | G ▷ C34 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C43 ◁ C33×C43 ◁ C34×C43 ◁ G | |
154 conjugacy classes of subgroups.
| minimal degree | μ(G) = 70 |
| transitive degree | μt(G) = 1161 |
A minimal faithful permutation representation — 2 generators on 70 points:
(1,2,5,4,8,15,13,7,19)(3,9,14,12,18,24,11,6,16)(10,17,23,21,20,27,22,26,25)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70);(1,3,10,4,12,21,13,11,22)(2,6,17,8,9,20,7,18,26)(5,14,23,15,24,27,19,16,25)1763 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 36);