Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#23761593 |
| Sylow | C79 ⋊ C2×#1420 |
286 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 115 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)(82,84,89,100)(83,90,94,116)(85,102,107,131)(86,99,88,97)(87,109,111,129)(91,118,121,127)(92,122,112,114)(93,123,124,125)(95,101,128,138)(96,105,132,142)(98,103,134,110)(104,140,106,139)(108,115,119,144)(113,117,130,141)(120,133,137,145)(126,143,135,136);(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)(82,83,86,92,89,94,88,112)(84,95,97,126,100,128,99,135)(85,101,104,136,107,138,106,143)(87,108,103,124,111,119,110,93)(90,113,114,96,116,130,122,132)(91,117,120,142,121,141,137,105)(98,133,129,118,134,145,109,127)(102,123,139,144,131,125,140,115);(80,81)1768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90039);