Finite Group DatabasebetaFinite Group Databasebeta| order | 34263 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C47 · Schur multiplier (H2) = C3 |
| direct product | C47×#10624514 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C47 | #6867 |
| commutator | C3×C9 | C3×C9×C47 |
| Frattini, cosocle | C32×C9 | C32×C47 |
| prime radical | C33×C47 | 3−1+2 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C47 ◁ C3×C9×C47 ◁ C32×C9×C47 ◁ G | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 128 |
| transitive degree | μt(G) = 3807 |
A minimal faithful permutation representation — 2 generators on 128 points:
(1,2,7,5,9,25,20,32,57,6,11,26,21,33,58,17,47,54,22,10,34,4,16,24,18,46,55)(3,12,35,14,38,68,44,30,67,15,39,70,19,37,23,48,8,27,45,29,60,50,66,53,51,31,56)(13,40,59,42,63,81,76,36,71,43,72,80,41,28,61,75,62,52,77,73,78,49,64,69,74,65,79)(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);(1,3,13)(2,8,28,10,30,63,11,31,64)(4,14,41)(5,19,49)(6,15,43)(7,23,52,26,53,79,34,68,71)(9,12,36,16,29,65,33,39,62)(17,44,74)(18,48,76)(20,51,75)(21,50,42)(22,45,77)(24,27,59,25,56,80,58,67,78)(32,37,40,46,38,73,47,66,72)(35,69,57,70,81,54,60,61,55)2679 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34263, 74);