Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#23761584 |
| Sylow | C79 ⋊ C2×#1417 |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 145 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 145 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(82,84)(83,89)(85,102)(86,97)(87,109)(88,100)(90,116)(91,112)(92,121)(93,123)(94,114)(95,101)(96,105)(98,103)(99,107)(104,135)(106,137)(108,113)(110,128)(111,115)(117,129)(118,144)(119,143)(120,141)(122,145)(124,132)(125,134)(126,142)(127,140)(130,138)(131,133)(136,139);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(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)(82,83,86,91,88,94,107,93)(84,95,97,124,100,125,99,131)(85,101,104,132,106,134,139,133)(87,108,103,92,110,120,138,122)(89,111,112,127,114,126,123,96)(90,115,117,140,119,142,118,105)(98,129,128,143,130,144,109,116)(102,121,135,141,137,145,136,113);(80,81)1792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90019);