Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C24 |
| direct product | C79×#25494 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C23×C79 | C2×#41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G | |
616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 4 generators on 119 points:
(1,2)(3,7)(4,5)(6,8)(9,10,15,29,13,18,14,19)(11,20,30,32,22,16,23,36)(12,24,28,17,26,35,27,34)(21,37,39,33,25,40,38,31)(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);(2,5)(6,7)(9,11,15,30,13,22,14,23)(10,16,29,36,18,20,19,32)(12,25,28,38,26,21,27,39)(17,33,35,40,34,31,24,37);(2,5)(6,7)(9,12,13,26)(10,17,18,34)(11,21,22,25)(14,28,15,27)(16,31,20,33)(19,35,29,24)(23,39,30,38)(32,37,36,40);(1,3,4,8)(2,6,5,7)(10,18)(16,20)(17,34)(19,29)(24,35)(31,33)(32,36)(37,40)3397 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 18482);