Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#23761603 |
| Sylow | C79 ⋊ C2×#1425 |
182 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 107 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:
(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)(82,84,96,123,87,99,104,111,86,98,115,139,107,129,106,128,89,101,125,144,109,131,105,127,88,100,124,143,103,126,85,97)(83,90,102,121,93,113,134,132,110,138,136,145,137,141,117,122,94,114,135,142,118,140,116,120,92,112,133,130,108,119,91,95);(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)(82,83,86,92,89,94,88,110)(84,95,98,120,101,122,100,132)(85,102,104,133,106,135,105,136)(87,108,107,118,109,137,103,93)(90,111,112,128,114,127,138,97)(91,115,116,125,117,124,134,96)(99,130,129,142,131,145,126,121)(113,123,119,139,140,144,141,143);(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, 90078);