Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#18719 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C79 |
| prime radical | #532×C79 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G | |
928 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 4 generators on 119 points:
(2,5)(3,7)(6,8)(9,10,14,18)(11,19,23,30)(12,16,26,34)(13,27,28,17)(15,21,31,22)(20,35,37,40)(24,33,25,32)(29,38,39,36)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(3,7)(5,8)(9,11)(10,15)(12,20)(13,21)(14,23)(16,29)(17,30)(18,31)(19,27)(22,28)(24,36)(25,38)(26,37)(32,35)(33,40)(34,39);(1,2)(3,8)(4,6)(5,7)(9,12,14,26)(10,16,18,34)(11,20,23,37)(13,25,28,24)(15,29,31,39)(17,33,27,32)(19,35,30,40)(21,38,22,36);(9,13,14,28)(10,17,18,27)(11,21,23,22)(12,24,26,25)(15,30,31,19)(16,32,34,33)(20,36,37,38)(29,35,39,40)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 11707);