Finite Group Databasebeta

← Group #10604992

Character table — Group #10604992

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111222244444444488888888888888101010101010202020202020202020404040404040
order12222244451010102020202024101010101010202020202020224444288888888444444
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
χ511111111111111111-1-111-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1
χ611111111111111111-1-111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ91111-1-1-1-111111-1-1-1-11-1-1-1111111-1-1-1-111-1-111-111-1-111-1-11-11-11-1
χ101111-1-1-1-111111-1-1-1-11-1-1-1111111-1-1-1-111-1-111-1-1-111-1-1111-1-11-11
χ111111-1-1-1-111111-1-1-1-11-1-1-1111111-1-1-1-1-1-111-1-11ii−i−i−i−iii-11i−i−ii
χ121111-1-1-1-111111-1-1-1-11-1-1-1111111-1-1-1-1-1-111-1-11−i−iiiii−i−i-11−iii−i
χ131111-1-1-1-111111-1-1-1-1-11-1-1-1-1-1-111111111-1-111-111-1-111-1-1-11-11-11
χ141111-1-1-1-111111-1-1-1-1-11-1-1-1-1-1-111111111-1-111-1-1-111-1-111-111-11-1
χ151111-1-1-1-111111-1-1-1-1-11-1-1-1-1-1-1111111-1-111-1-11ii−i−i−i−iii1-1−iii−i
χ161111-1-1-1-111111-1-1-1-1-11-1-1-1-1-1-1111111-1-111-1-11−i−iiiii−i−i1-1i−i−ii
χ17222222-2-2-22222-2-2-2-200220000-2-2000022-2-2-2-2200000000000000
χ18222222-2-2-22222-2-2-2-200220000-2-20000-2-22222-200000000000000
χ192222-2-222-22222222200-2-20000-2-200002222-2-2-200000000000000
χ202222-2-222-22222222200-2-20000-2-20000-2-2-2-222200000000000000
χ2122-2-2002i−2i022-2-22i2i−2i−2i000000000000002-22i−2i000i2−i22−2i2−i22−2000000
χ2222-2-2002i−2i022-2-22i2i−2i−2i000000000000002-22i−2i000−i2i2−22−i2i2−22000000
χ2322-2-2002i−2i022-2-22i2i−2i−2i00000000000000-22−2i2i0002−2−i2i2−22i2−i2000000
χ2422-2-2002i−2i022-2-22i2i−2i−2i00000000000000-22−2i2i000−22i2−i22−2−i2i2000000
χ2522-2-200−2i2i022-2-2−2i−2i2i2i000000000000002-2−2i2i000i2−i2−22i2−i2−22000000
χ2622-2-200−2i2i022-2-2−2i−2i2i2i000000000000002-2−2i2i000−i2i22−2−i2i22−2000000
χ2722-2-200−2i2i022-2-2−2i−2i2i2i00000000000000-222i−2i0002−2i2−i2−22−i2i2000000
χ2822-2-200−2i2i022-2-2−2i−2i2i2i00000000000000-222i−2i000−22−i2i22−2i2−i2000000
χ29444444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ30444444444-1-1-1-1-1-1-1-1-4-4-1-11111-1-11111000000000000000000000
χ31444444-4-4-4-1-1-1-1111100-1-155−5−51155−5−5000000000000000000000
χ32444444-4-4-4-1-1-1-1111100-1-1−5−55511−5−555000000000000000000000
χ334444-4-444-4-1-1-1-1-1-1-1-1001155−5−511−5−555000000000000000000000
χ344444-4-444-4-1-1-1-1-1-1-1-10011−5−5551155−5−5000000000000000000000
χ354444-4-4-4-44-1-1-1-111114-411-1-1-1-1-1-11111000000000000000000000
χ364444-4-4-4-44-1-1-1-11111-44111111-1-1-1-1-1-1000000000000000000000
χ374-44-4000004-44-400000000000000000000004i−4i000000000000000
χ384-44-4000004-44-40000000000000000000000−4i4i000000000000000
χ394-4-444-40004-4-440000004-40000000000000000000000000000000
χ404-4-444-4000-111-15−55−500-11−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ365−5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36000000000000000000000
χ414-4-444-4000-111-15−55−500-11ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ365−5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36000000000000000000000
χ424-4-444-4000-111-1−55−5500-11−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−55−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36000000000000000000000
χ434-4-444-4000-111-1−55−5500-11ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−55ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36000000000000000000000
χ444-4-44-440004-4-44000000-440000000000000000000000000000000
χ454-4-44-44000-111-15−55−5001-1−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−55ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36000000000000000000000
χ464-4-44-44000-111-15−55−5001-1ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−55−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36000000000000000000000
χ474-4-44-44000-111-1−55−55001-1−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ365−5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36000000000000000000000
χ484-4-44-44000-111-1−55−55001-1ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ365−5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36000000000000000000000
χ4988-8-8008i−8i0-2-222−2i−2i2i2i00000000000000000000000000000000000
χ5088-8-800−8i8i0-2-2222i2i−2i−2i00000000000000000000000000000000000
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.