Finite Group DatabasebetaFinite Group Databasebeta| order | 29889 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C41 · Schur multiplier (H2) = C3×C9 |
| direct product | C41×#10624535 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C41 | #6879 |
| commutator, Frattini, cosocle | C92 | C32×C41 |
| LCS | G ▷ C92 ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C41 ◁ C32×C41 ◁ C3×C9×C41 ◁ C92×C41 ◁ G | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 122 |
| transitive degree | μt(G) = 3321 |
A minimal faithful permutation representation — 2 generators on 122 points:
(1,2,6)(3,11,18)(4,9,19)(5,10,22)(7,23,13)(8,27,36)(12,35,43)(14,34,46)(15,30,47)(16,28,20)(17,31,21)(24,54,65)(25,51,39)(26,44,40)(29,49,64)(32,50,37)(33,52,63)(38,62,71)(41,57,45)(42,59,48)(53,68,58)(55,70,67)(56,73,78)(60,69,66)(61,72,79)(74,80,76)(75,81,77)(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);(1,3,12,36,63,78,16,40,66,5,14,38,64,79,81,42,68,80,17,41,67,15,39,65,4,13,37)(2,7,24,30,57,76,59,61,62,10,26,56,8,11,32,9,25,55,31,58,77,29,34,60,28,33,35)(6,18,43,27,52,73,20,44,69,22,46,71,49,72,75,48,53,74,21,45,70,47,51,54,19,23,50)3649 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29889, 95);