Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#23761615 |
| Sylow | C79 ⋊ C2×SD128 |
134 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(83,89)(84,95)(85,96)(86,101)(87,105)(90,91)(92,120)(93,122)(94,111)(97,128)(98,131)(99,112)(100,108)(102,136)(103,116)(104,109)(106,119)(107,110)(113,133)(114,132)(115,118)(117,138)(121,145)(123,124)(125,129)(126,127)(130,144)(134,141)(135,140)(137,143)(139,142);(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)(82,83,88,94)(84,89,99,111)(85,100,103,134)(86,104,106,137)(87,107,105,93)(90,112,115,95)(91,116,118,96)(92,119,121,101)(97,120,130,145)(98,122,129,110)(102,135,126,133)(108,139,141,124)(109,142,143,123)(113,144,140,128)(114,125,138,131)(117,127,132,136);(80,81)1552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90614);