Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C79 · Schur multiplier (H2) = C27 |
| direct product | C79×#36701 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C79 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C79 |
| socle, prime radical | C23×C79 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C79 ◁ G | |
1304 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 5 generators on 119 points:
(1,2)(3,6)(4,5)(7,8)(9,10,13,16)(11,14,18,22)(12,15,20,24)(17,21,19,23)(25,26,30,33)(27,34,37,31)(28,38,29,32)(35,39,36,40)(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);(9,11,13,18)(10,14,16,22)(12,19,20,17)(15,23,24,21)(25,27,30,37)(26,31,33,34)(28,36,29,35)(32,40,38,39);(2,5)(6,8)(9,12)(10,15)(11,17)(13,20)(14,21)(16,24)(18,19)(22,23)(25,28,30,29)(26,32,33,38)(27,35,37,36)(31,39,34,40);(10,16)(12,20)(14,22)(17,19)(25,28,30,29)(26,32,33,38)(27,36,37,35)(31,40,34,39);(1,3,4,7)(2,6,5,8)(25,29,30,28)(26,32,33,38)(27,35,37,36)(31,40,34,39)4108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 29689);