Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | #1425×D79 |
| Fitting | C79×#1425 ⋊ C2 |
| Sylow | C79 ⋊ C2×#1425 |
182 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 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);(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)(80,82,94,121,85,97,102,109,84,96,113,137,105,127,104,126,87,99,123,142,107,129,103,125,86,98,122,141,101,124,83,95)(81,88,100,119,91,111,132,130,108,136,134,143,135,139,115,120,92,112,133,140,116,138,114,118,90,110,131,128,106,117,89,93);(80,81,84,90,87,92,86,108)(82,93,96,118,99,120,98,130)(83,100,102,131,104,133,103,134)(85,106,105,116,107,135,101,91)(88,109,110,126,112,125,136,95)(89,113,114,123,115,122,132,94)(97,128,127,140,129,143,124,119)(111,121,117,137,138,142,139,141)1558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90077);