Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ #7464 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 2 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)(80,82,95,110,85,98,83,96,109,136,103,131,102,97,134,141,87,100,129,130,107,137,105,133,86,99,128,142,84,106,104,132)(81,88,111,135,90,113,89,94,91,114,101,124,117,122,118,125,93,116,138,143,121,112,120,127,92,115,139,123,108,140,119,126);(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)(80,81,84,90,86,91,107,117,87,93,102,121,109,92,85,108)(82,94,97,123,99,125,98,135,100,127,106,124,136,126,137,143)(83,101,95,118,104,138,128,120,105,139,129,119,134,111,103,89)(88,110,112,141,114,142,140,96,116,130,113,132,115,131,122,133)Polycyclic presentation:
2^8,79|a^2=d,b^2=ceg,c^2=egh,d^2=f,e^2=gh,f^2=h,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,d^b=dh,i^b=i^781768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57252);