Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ #7454 |
96 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)(81,89,94,119)(83,97)(84,108)(85,100)(86,114)(87,98)(88,101)(90,120,123,140)(91,124,126,131)(92,127,112,117)(93,129,113,130)(95,125,132,122)(96,105)(99,115)(102,116,141,143)(103,136)(104,138)(106,137)(107,139)(109,133)(110,134)(111,135)(118,121,142,128);(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)(80,81,84,91,109,93,104,90,85,112,110,122,115,121,107,141,88,94,105,126,86,113,106,123,87,92,111,125,103,128,83,102)(82,95,97,117,136,120,135,129,98,124,137,89,114,116,96,118,101,132,139,127,99,140,134,130,100,131,138,119,133,143,108,142)Polycyclic presentation:
2^8,79|a^2=d,b^2=eg,c^2=fgh,d^2=efgh,e^2=h,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=eh,f^a=fh,i^a=i^78,c^b=cf,d^b=def,e^b=eh,f^b=fg,g^b=gh1519 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57231);