Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ #7462 |
78 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)(80,82,95,124,85,98,125,143,108,132,136,138,106,130,104,128,87,100,126,137,105,129,103,127,86,99,102,109,84,97,83,96)(81,88,101,120,90,110,114,121,91,111,133,141,117,139,116,123,93,113,135,142,118,140,115,122,92,112,134,131,107,119,89,94);(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)(80,81,84,90,86,91,105,117,87,93,106,118,108,92,85,107)(82,94,97,120,99,121,129,141,100,123,130,142,132,122,98,131)(83,101,102,114,103,133,126,116,104,135,136,115,125,134,95,89)(88,109,110,127,111,137,139,128,113,138,140,143,112,124,119,96)Polycyclic presentation:
2^8,79|a^2=d,b^2=ce,c^2=eg,d^2=f,e^2=gh,f^2=h,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^b=i^781792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57248);