Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ #7544 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 2 generators on 143 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)(80,82,83,96,88,99,87,86)(81,89,90,95,94,93,100,115)(84,97,101,110,106,125,105,104)(85,98,102,123,109,126,108,107)(91,111,113,121,118,117,127,136)(92,112,114,122,120,119,128,137)(103,124,129,133,132,141,131,130)(116,134,135,140,139,138,142,143);(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)(80,81,84,91,85,92,103,116,86,93,104,117,107,119,130,138,87,90,105,113,108,114,131,135,99,115,125,136,126,137,141,143,88,94,106,118,109,120,132,139,96,89,110,111,123,112,133,134,83,100,101,127,102,128,129,142,82,95,97,121,98,122,124,140)Polycyclic presentation:
2^8,79|a^2=d,b^2=c,c^2=h,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bc,c^a=ch,i^a=i^785104 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57466);