Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #1420×D79 |
| Fitting | C79×#1420 ⋊ C2 |
| Sylow | C79 ⋊ C2×#1420 |
286 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 286 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)(80,82,87,98)(81,88,92,114)(83,100,105,129)(84,97,86,95)(85,107,109,127)(89,116,119,125)(90,120,110,112)(91,121,122,123)(93,99,126,136)(94,103,130,140)(96,101,132,108)(102,138,104,137)(106,113,117,142)(111,115,128,139)(118,131,135,143)(124,141,133,134);(80,81,84,90,87,92,86,110)(82,93,95,124,98,126,97,133)(83,99,102,134,105,136,104,141)(85,106,101,122,109,117,108,91)(88,111,112,94,114,128,120,130)(89,115,118,140,119,139,135,103)(96,131,127,116,132,143,107,125)(100,121,137,142,129,123,138,113)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90037);