Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#23761536 |
| Sylow | C79 ⋊ C2×#1398 |
222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 113 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)(83,88,90,92)(84,93)(89,102,103,100)(91,101,105,106)(94,107)(95,99)(104,112,113,111)(108,110);(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)(82,83,84,89,85,91,94,104,86,92,95,102,96,106,108,112,87,90,93,103,97,105,107,113,98,88,99,100,109,101,110,111);(80,81)3208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89753);