Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C24 |
| direct product | C79×#26995 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | #537×C79 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ G | |
762 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)(3,7)(4,6)(5,8)(9,10)(11,22)(12,18)(13,27)(14,32)(15,20)(16,21)(17,24)(19,29)(23,35)(25,34)(26,39)(28,37)(30,36)(31,40)(33,38)(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);(1,3,4,8)(2,5,6,7)(9,11,14,24,16,25,15,12)(10,17,20,22,21,18,32,34)(13,23,29,28,31,38,30,26)(19,33,27,37,36,35,40,39);(2,6)(3,8)(9,12)(10,18)(11,14)(13,28)(15,25)(16,24)(17,21)(19,33)(20,34)(22,32)(23,30)(26,31)(27,37)(29,38)(35,36)(39,40);(2,6)(5,7)(9,13,15,30,16,31,14,29)(10,19,32,40,21,36,20,27)(11,23,12,26,25,38,24,28)(17,33,34,39,18,35,22,37)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 19983);