Finite Group DatabasebetaFinite Group Databasebeta| order | 34263 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9×C47 · Schur multiplier (H2) = C32 |
| direct product | C47×#10624709 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C47 | C9⋊C9 |
| commutator | C9 | C32×C9×C47 |
| Frattini, cosocle | C3×C9 | C33×C47 |
| socle | C3×C47 | C3×C9⋊C9 |
| prime radical | C33×C47 | 3−1+2 |
| LCS | G ▷ C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9×C47 ◁ C32×C9×C47 ◁ G | |
198 conjugacy classes of subgroups.
| minimal degree | μ(G) = 128 |
| transitive degree | μt(G) = 3807 |
A minimal faithful permutation representation — 3 generators on 128 points:
(1,2,7)(3,11,31,15,34,65,45,69,58)(4,9,23)(5,18,47)(6,10,25)(8,26,40,28,51,41,62,77,43)(12,35,57,38,70,80,39,71,78)(13,33,22,14,42,52,44,76,64)(16,29,53)(17,46,55)(19,49,54)(20,48,24)(21,30,56)(27,59,37,60,81,36,61,63,74)(32,66,73,67,79,72,68,50,75)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128);(1,3,12,5,14,37,19,43,75,6,15,39,20,44,74,16,40,72,21,45,38,4,13,36,17,41,73)(2,8,27,9,11,32,29,33,35,10,28,61,18,34,68,46,42,71,30,62,60,48,69,67,49,76,70)(7,22,50,24,26,57,55,58,59,25,52,79,23,51,78,54,31,63,56,64,66,47,77,80,53,65,81);(1,4,16,6,5,17,21,20,19)(2,9,29,10,18,46,30,48,49)(3,13,40,15,14,41,45,44,43)(7,23,53,25,47,55,56,24,54)(8,11,33,28,34,42,62,69,76)(12,36,72,39,37,73,38,74,75)(22,51,65,52,77,58,64,26,31)(27,32,35,61,68,71,60,67,70)(50,78,81,79,80,59,66,57,63)4935 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34263, 269);