Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C24 |
| direct product | C79×#26848 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | #535×C79 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ G | |
718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 4 generators on 119 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,22)(12,28)(13,32)(14,20)(15,21)(16,25)(17,30)(18,33)(19,34)(23,37)(24,40)(26,35)(27,39)(29,38)(31,36)(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);(9,11,14,25,15,27,34,26)(10,16,19,22,21,35,20,39)(12,29,30,13,24,33,31,23)(17,18,28,32,36,38,40,37);(2,5)(6,8)(9,12,14,30,15,24,34,31)(10,17,19,28,21,36,20,40)(11,23,25,29,27,13,26,33)(16,32,22,38,35,37,39,18);(1,3,4,7)(2,6,5,8)(9,13,14,33,15,23,34,29)(10,18,19,32,21,38,20,37)(11,24,25,31,27,12,26,30)(16,28,22,36,35,40,39,17)3634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 19836);