Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×#23761542 |
| Sylow | C79 ⋊ C2×#1401 |
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)(83,90)(85,101)(86,104)(87,99)(88,97)(89,100)(91,114)(92,117)(93,112)(94,96)(95,113)(98,107)(102,125)(103,129)(105,132)(106,110)(108,126)(109,128)(111,120)(115,123)(116,138)(118,140)(119,131)(121,124)(122,137)(127,134)(130,144)(133,135)(136,142)(139,143)(141,145);(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)(82,83,86,92,87,93,105,118,88,94,106,119,108,121,133,141,89,95,107,120,109,122,134,142,85,91,102,115,103,116,130,139)(84,96,98,123,99,124,127,143,97,113,125,117,126,137,144,140,100,114,104,131,128,138,132,145,101,90,110,111,129,112,135,136);(80,81)3232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89775);