Finite Group Databasebeta

← Group #10604429

Character table — Group #10604429

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111222244444444488888888888888101010101010202020202020202020404040404040
order12224444451010102020202044202020202020202020202020224444488888888444444
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ41111111111111111111111111111111-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ511111111111111111-1-11111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1
χ611111111111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ91111-1-1-1-111111-1-1-1-11-111-1-11111-1-1-1-111-1-111-111-1-111-1-11-11-11-1
χ101111-1-1-1-111111-1-1-1-11-111-1-11111-1-1-1-111-1-111-1-1-111-1-1111-1-11-11
χ111111-1-1-1-111111-1-1-1-11-111-1-11111-1-1-1-1-1-111-1-11ii−i−i−i−iii-11i−i−ii
χ121111-1-1-1-111111-1-1-1-11-111-1-11111-1-1-1-1-1-111-1-11−i−iiiii−i−i-11−iii−i
χ131111-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1-1111111-1-111-111-1-111-1-1-11-11-11
χ141111-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1-1111111-1-111-1-1-111-1-111-111-11-1
χ151111-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1-11111-1-111-1-11ii−i−i−i−iii1-1−iii−i
χ161111-1-1-1-111111-1-1-1-1-1111-1-1-1-1-1-11111-1-111-1-11−i−iiiii−i−i1-1i−i−ii
χ17222222-2-2-22222222200-2-2-2-2000000002222-2-2-200000000000000
χ18222222-2-2-22222222200-2-2-2-200000000-2-2-2-222200000000000000
χ192222-2-222-22222-2-2-2-200-2-2220000000022-2-2-2-2200000000000000
χ202222-2-222-22222-2-2-2-200-2-22200000000-2-22222-200000000000000
χ2122-2-22-200022-2-222-2-2000000000000002-22-20002−22−22−22−2000000
χ2222-2-22-200022-2-222-2-2000000000000002-22-2000−22−22−22−22000000
χ2322-2-22-200022-2-222-2-200000000000000-22-22000i2−i2i2−i2−i2i2−i2i2000000
χ2422-2-22-200022-2-222-2-200000000000000-22-22000−i2i2−i2i2i2−i2i2−i2000000
χ2522-2-2-2200022-2-2-2-222000000000000002-2-220002−2−222−2−22000000
χ2622-2-2-2200022-2-2-2-222000000000000002-2-22000−222−2−222−2000000
χ2722-2-2-2200022-2-2-2-22200000000000000-222-2000i2−i2−i2i2−i2i2i2−i2000000
χ2822-2-2-2200022-2-2-2-22200000000000000-222-2000−i2i2i2−i2i2−i2−i2i2000000
χ29444444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ30444444444-1-1-1-1-1-1-1-1-4-4-1-1-1-111111111000000000000000000000
χ31444444-4-4-4-1-1-1-1-1-1-1-100111155−5−555−5−5000000000000000000000
χ32444444-4-4-4-1-1-1-1-1-1-1-1001111−5−555−5−555000000000000000000000
χ334444-4-444-4-1-1-1-111110011-1-155−5−5−5−555000000000000000000000
χ344444-4-444-4-1-1-1-111110011-1-1−5−55555−5−5000000000000000000000
χ354444-4-4-4-44-1-1-1-111114-4-1-111-1-1-1-11111000000000000000000000
χ364444-4-4-4-44-1-1-1-11111-44-1-1111111-1-1-1-1000000000000000000000
χ374-44-4000004-44-400000000000000000000004i−4i000000000000000
χ384-44-4000004-44-40000000000000000000000−4i4i000000000000000
χ394-4-44004i−4i04-4-44000000004i−4i00000000000000000000000000000
χ404-4-44004i−4i0-111-1i5−i5i5−i5005−5−ii−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36000000000000000000000
χ414-4-44004i−4i0-111-1i5−i5i5−i5005−5−iiζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36000000000000000000000
χ424-4-44004i−4i0-111-1−i5i5−i5i500−55−iiζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36000000000000000000000
χ434-4-44004i−4i0-111-1−i5i5−i5i500−55−ii−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36000000000000000000000
χ444-4-4400−4i4i04-4-4400000000−4i4i00000000000000000000000000000
χ454-4-4400−4i4i0-111-1i5−i5i5−i500−55i−iζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36000000000000000000000
χ464-4-4400−4i4i0-111-1i5−i5i5−i500−55i−i−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36000000000000000000000
χ474-4-4400−4i4i0-111-1−i5i5−i5i5005−5i−i−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36000000000000000000000
χ484-4-4400−4i4i0-111-1−i5i5−i5i5005−5i−iζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36000000000000000000000
χ4988-8-88-8000-2-222-2-22200000000000000000000000000000000000
χ5088-8-8-88000-2-22222-2-200000000000000000000000000000000000
χ518-88-800000-22-222i5−2i5−2i52i500000000000000000000000000000000000
χ528-88-800000-22-22−2i52i52i5−2i500000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.