Finite Group DatabasebetaFinite Group Databasebeta| order | 29889 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C41 · Schur multiplier (H2) = C3 |
| direct product | C41×#10624517 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C41 | #6867 |
| commutator | C3×C9 | C3×C9×C41 |
| Frattini, cosocle | C32×C9 | C32×C41 |
| prime radical | C33×C41 | 3−1+2 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C41 ◁ C3×C9×C41 ◁ C32×C9×C41 ◁ G | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 122 |
| transitive degree | μt(G) = 3321 |
A minimal faithful permutation representation — 2 generators on 122 points:
(1,2,7,5,10,27,23,36,62,24,11,40,55,38,71,21,9,34,6,12,28,20,39,61,4,18,26)(3,13,41,16,32,70,19,43,25,51,44,58,54,33,60,15,37,74,17,35,72,22,8,29,53,31,59)(14,45,77,47,42,76,46,68,80,78,69,63,56,65,57,52,30,64,48,66,79,50,73,81,49,67,75)(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);(1,3,14)(2,8,30,11,32,67,12,33,68)(4,19,52)(5,22,56)(6,17,48)(7,25,57,28,59,76,40,74,81)(9,35,73,18,13,42,36,44,65)(10,37,45,38,31,69,39,43,66)(15,49,23)(16,50,55)(20,54,47)(21,53,46)(24,51,78)(26,60,77,34,70,79,62,29,63)(27,41,75,61,72,64,71,58,80)2337 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29889, 77);