Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C43 · Schur multiplier (H2) = C38 |
| direct product | C43×#10624562 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C43 | C33 |
| commutator, Frattini, cosocle | C33 | C33×C43 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C33×C43 ◁ G | |
2138 conjugacy classes of subgroups.
| minimal degree | μ(G) = 70 |
| transitive degree | μt(G) = 10449 |
A minimal faithful permutation representation — 3 generators on 70 points:
(1,2,4)(3,6,8)(5,9,7)(10,11,13)(12,15,17)(14,18,16)(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);(2,5,6)(4,8,9)(19,20,22)(21,24,26)(23,27,25);(11,14,15)(13,17,18)(20,23,24)(22,26,27)4515 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 122);