Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #1417×D79 |
| Fitting | C79×#1417 ⋊ C2 |
| Sylow | C79 ⋊ C2×#1417 |
294 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 294 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)(81,87)(83,100)(84,95)(85,107)(86,98)(88,114)(89,110)(90,119)(91,121)(92,112)(93,99)(94,103)(96,101)(97,105)(102,133)(104,135)(106,111)(108,126)(109,113)(115,127)(116,142)(117,141)(118,139)(120,143)(122,130)(123,132)(124,140)(125,138)(128,136)(129,131)(134,137);(80,81,84,89,86,92,105,91)(82,93,95,122,98,123,97,129)(83,99,102,130,104,132,137,131)(85,106,101,90,108,118,136,120)(87,109,110,125,112,124,121,94)(88,113,115,138,117,140,116,103)(96,127,126,141,128,142,107,114)(100,119,133,139,135,143,134,111)1558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90017);