Finite Group Databasebeta

← Group #13017052

Character table — Group #13017052

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size11112222444444444555588888888101010101010101010101010101010101616161616161616162020202020202020202020202020203232404040404040404040404040
order12222244458888101010222224441010202022444444444444442020202020404040404448888888888881020244444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111-1-1-1-111111111-1-1ii−i−iiiii−i−i−i−i-1-1111111111-1i−i-1-1-1-1iiii−i−i−i−i11-1-1-1-1i−ii−iii−i−i
χ611111111111111111-1-1-1-111111111-1-1−i−iii−i−i−i−iiiii-1-1111111111-1−ii-1-1-1-1−i−i−i−iiiii11-1-1-1-1−ii−ii−i−iii
χ711111111111111111-1-1-1-1-1-1-1-11111-1-1ii−i−iiiii−i−i−i−i-1-11-1-1-1-11111-1i−i-1-1-1-1iiii−i−i−i−i-1-11111−ii−ii−i−iii
χ811111111111111111-1-1-1-1-1-1-1-11111-1-1−i−iii−i−i−i−iiiii-1-11-1-1-1-11111-1−ii-1-1-1-1−i−i−i−iiiii-1-11111i−ii−iii−i−i
χ91111111111-1-1-1-1111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ101111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-11111
χ111111111111-1-1-1-11111111-1-1111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ121111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1
χ131111111111-1-1-1-1111-1-1-1-111-1-11111-1-1ii−i−iiiii−i−i−i−i-1-11-1-1-1-1-1-1-1-1-1i−i1111−i−i−i−iiiii11-1-111i−ii−i−i−iii
χ141111111111-1-1-1-1111-1-1-1-111-1-11111-1-1−i−iii−i−i−i−iiiii-1-11-1-1-1-1-1-1-1-1-1−ii1111iiii−i−i−i−i11-1-111−ii−iiii−i−i
χ151111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1ii−i−iiiii−i−i−i−i-1-111111-1-1-1-1-1i−i1111−i−i−i−iiiii-1-111-1-1−ii−iiii−i−i
χ161111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1−i−iii−i−i−i−iiiii-1-111111-1-1-1-1-1−ii1111iiii−i−i−i−i-1-111-1-1i−ii−i−i−iii
χ171111-1-1-1-111ii−i−i11111111-1i−i-1-1-1-1-1-1111111-1-111-1-1-1-11ii−i−iii−i−i1-1-1ii−i−iii−i−iii−i−i1-11-1i−i-1-111i−ii−i
χ181111-1-1-1-111ii−i−i11111111-1i−i-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11ii−i−iii−i−i111ii−i−i−i−iii−i−iii1-11-1i−i11-1-1−ii−ii
χ191111-1-1-1-111ii−i−i1111111-11−ii-1-1-1-1-1-1111111-1-111-1-1-1-11−i−iiiii−i−i1-1-1ii−i−iii−i−iii−i−i-11-11−ii11-1-1−ii−ii
χ201111-1-1-1-111ii−i−i1111111-11−ii-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11−i−iiiii−i−i111ii−i−i−i−iii−i−iii-11-11−ii-1-111i−ii−i
χ211111-1-1-1-111ii−i−i111-1-1-1-11-1i−i-1-1-1-111ii−i−iii−i−i−i−iii111ii−i−iii−i−i-1−ii−i−iii-1-11111-1-11-1-11−ii−iii−i-111-1
χ221111-1-1-1-111ii−i−i111-1-1-1-11-1i−i-1-1-1-111−i−iii−i−iiiii−i−i111ii−i−iii−i−i-1i−i−i−iii11-1-1-1-1111-1-11−iii−i−ii1-1-11
χ231111-1-1-1-111ii−i−i111-1-1-1-1-11−ii-1-1-1-111ii−i−iii−i−i−i−iii111−i−iiiii−i−i-1−ii−i−iii-1-11111-1-1-111-1i−ii−i−ii1-1-11
χ241111-1-1-1-111ii−i−i111-1-1-1-1-11−ii-1-1-1-111−i−iii−i−iiiii−i−i111−i−iiiii−i−i-1i−i−i−iii11-1-1-1-111-111-1i−i−iii−i-111-1
χ251111-1-1-1-111−i−iii11111111-1−ii-1-1-1-1-1-1111111-1-111-1-1-1-11−i−iii−i−iii1-1-1−i−iii−i−iii−i−iii1-11-1−ii-1-111−ii−ii
χ261111-1-1-1-111−i−iii11111111-1−ii-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11−i−iii−i−iii111−i−iiiii−i−iii−i−i1-11-1−ii11-1-1i−ii−i
χ271111-1-1-1-111−i−iii1111111-11i−i-1-1-1-1-1-1111111-1-111-1-1-1-11ii−i−i−i−iii1-1-1−i−iii−i−iii−i−iii-11-11i−i11-1-1i−ii−i
χ281111-1-1-1-111−i−iii1111111-11i−i-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11ii−i−i−i−iii111−i−iiiii−i−iii−i−i-11-11i−i-1-111−ii−ii
χ291111-1-1-1-111−i−iii111-1-1-1-11-1−ii-1-1-1-111ii−i−iii−i−i−i−iii111−i−iii−i−iii-1−iiii−i−i11-1-1-1-1111-1-11i−i−iii−i1-1-11
χ301111-1-1-1-111−i−iii111-1-1-1-11-1−ii-1-1-1-111−i−iii−i−iiiii−i−i111−i−iii−i−iii-1i−iii−i−i-1-11111-1-11-1-11i−ii−i−ii-111-1
χ311111-1-1-1-111−i−iii111-1-1-1-1-11i−i-1-1-1-111ii−i−iii−i−i−i−iii111ii−i−i−i−iii-1−iiii−i−i11-1-1-1-111-111-1−iii−i−ii-111-1
χ321111-1-1-1-111−i−iii111-1-1-1-1-11i−i-1-1-1-111−i−iii−i−iiiii−i−i111ii−i−i−i−iii-1i−iii−i−i-1-11111-1-1-111-1−ii−iii−i1-1-11
χ33222222-2-2-2200002222222000022-2-2222222-2-2-2-2-2-2-2-2-2-2-200000000-22200000000000000000000000000
χ34222222-2-2-2200002222222000022-2-222-2-2-2-222222222-2-2-200000000-2-2-200000000000000000000000000
χ35222222-2-2-220000222-2-2-2-2000022-2-2-2-22i2i−2i−2i−2i−2i−2i−2i2i2i2i2i22-20000000022i−2i00000000000000000000000000
χ36222222-2-2-220000222-2-2-2-2000022-2-2-2-2−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i22-2000000002−2i2i00000000000000000000000000
χ372222-2-222-22000022222220000-2-222-2-22222-2-222-2-22222-200000000-2-2-200000000000000000000000000
χ382222-2-222-22000022222220000-2-222-2-2-2-2-2-222-2-222-2-222-200000000-22200000000000000000000000000
χ392222-2-222-220000222-2-2-2-20000-2-222222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-2-2-2000000002−2i2i00000000000000000000000000
χ402222-2-222-220000222-2-2-2-20000-2-22222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-2-2-20000000022i−2i00000000000000000000000000
χ412-22-22-20002i2−i2i2−i2-22-222-2-200002-200-2200002i−2i2i−2i2i−2i2i−2i0000000i2−i2i2−i2000i2−i2i2−i22−22−22−22−200000000000000
χ422-22-22-20002i2−i2i2−i2-22-222-2-200002-200-220000−2i2i−2i2i−2i2i−2i2i0000000i2−i2i2−i2000i2−i2i2−i2−22−22−22−2200000000000000
χ432-22-22-20002i2−i2i2−i2-22-2-2-22200002-2002-200002-22-2-22-220000000i2−i2i2−i2000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000000000
χ442-22-22-20002i2−i2i2−i2-22-2-2-22200002-2002-20000-22-222-22-20000000i2−i2i2−i2000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000000000
χ452-22-22-20002−i2i2−i2i2-22-222-2-200002-200-2200002i−2i2i−2i2i−2i2i−2i0000000−i2i2−i2i2000−i2i2−i2i2−22−22−22−2200000000000000
χ462-22-22-20002−i2i2−i2i2-22-222-2-200002-200-220000−2i2i−2i2i−2i2i−2i2i0000000−i2i2−i2i2000−i2i2−i2i22−22−22−22−200000000000000
χ472-22-22-20002−i2i2−i2i2-22-2-2-22200002-2002-200002-22-2-22-220000000−i2i2−i2i2000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000000000
χ482-22-22-20002−i2i2−i2i2-22-2-2-22200002-2002-20000-22-222-22-20000000−i2i2−i2i2000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000000000
χ492-22-2-2200022−2−22-22-222-2-20000-22002-200002i−2i−2i2i2i−2i−2i2i00000002−2−220002−2−22−i2i2i2−i2−i2i2i2−i200000000000000
χ502-22-2-2200022−2−22-22-222-2-20000-22002-20000−2i2i2i−2i−2i2i2i−2i00000002−2−220002−2−22i2−i2−i2i2i2−i2−i2i200000000000000
χ512-22-2-2200022−2−22-22-2-2-2220000-2200-2200002-2-22-222-200000002−2−22000−222−2−222−22−2−2200000000000000
χ522-22-2-2200022−2−22-22-2-2-2220000-2200-220000-222-22-2-2200000002−2−22000−222−22−2−22−222−200000000000000
χ532-22-2-220002−222−2-22-222-2-20000-22002-200002i−2i−2i2i2i−2i−2i2i0000000−222−2000−222−2i2−i2−i2i2i2−i2−i2i200000000000000
χ542-22-2-220002−222−2-22-222-2-20000-22002-20000−2i2i2i−2i−2i2i2i−2i0000000−222−2000−222−2−i2i2i2−i2−i2i2i2−i200000000000000
χ552-22-2-220002−222−2-22-2-2-2220000-2200-2200002-2-22-222-20000000−222−20002−2−222−2−22−222−200000000000000
χ562-22-2-220002−222−2-22-2-2-2220000-2200-220000-222-22-2-220000000−222−20002−2−22−222−22−2−2200000000000000
χ57444444444-14444-1-1-100004444-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1000000000000000-1-1000000000000
χ58444444444-14444-1-1-10000-4-4-4-4-1-1-1-10000000000000000-11111-1-1-1-100000000000000011000000000000
χ59444444444-1-4-4-4-4-1-1-1000044-4-4-1-1-1-10000000000000000-111111111000000000000000-1-1000000000000
χ60444444444-1-4-4-4-4-1-1-10000-4-444-1-1-1-10000000000000000-1-1-1-1-1111100000000000000011000000000000
χ614444-4-4-4-44-14i4i−4i−4i-1-1-100004-44i−4i11110000000000000000-1−i−iii−i−iii000000000000000-11000000000000
χ624444-4-4-4-44-14i4i−4i−4i-1-1-10000-44−4i4i11110000000000000000-1ii−i−i−i−iii0000000000000001-1000000000000
χ634444-4-4-4-44-1−4i−4i4i4i-1-1-100004-4−4i4i11110000000000000000-1ii−i−iii−i−i000000000000000-11000000000000
χ644444-4-4-4-44-1−4i−4i4i4i-1-1-10000-444i−4i11110000000000000000-1−i−iiiii−i−i0000000000000001-1000000000000
χ6544-4-4004i−4i0400004-4-44-4-440000004i−4i000000000000004i−4i00000000000000000000000000000000000000
χ6644-4-4004i−4i0400004-4-4-444-40000004i−4i00000000000000−4i4i00000000000000000000000000000000000000
χ6744-4-400−4i4i0400004-4-44-4-44000000−4i4i00000000000000−4i4i00000000000000000000000000000000000000
χ6844-4-400−4i4i0400004-4-4-444-4000000−4i4i000000000000004i−4i00000000000000000000000000000000000000
χ694-4-440000040000-4-444-44-400000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ704-4-440000040000-4-444-44-40000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ714-4-440000040000-4-44-44-4400000000004-4-44000000000000000000000000000000000000000000000000
χ724-4-440000040000-4-44-44-440000000000-444-4000000000000000000000000000000000000000000000000
χ73888888-8-8-8-20000-2-2-200000000-2-222000000000000000020000000000000000000000000000000000000
χ748888-8-888-8-20000-2-2-20000000022-2-2000000000000000020000000000000000000000000000000000000
χ7588-8-8008i−8i0-20000-2220000000000−2i2i00000000000000000ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ38000000000000000000000000000000000
χ7688-8-8008i−8i0-20000-2220000000000−2i2i00000000000000000−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38000000000000000000000000000000000
χ7788-8-800−8i8i0-20000-22200000000002i−2i00000000000000000ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ38000000000000000000000000000000000
χ7888-8-800−8i8i0-20000-22200000000002i−2i00000000000000000−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ38000000000000000000000000000000000
χ798-88-88-8000-24i2−4i24i2−4i22-2200000000-2200000000000000000000000−i2i2−i2i200000000000000000000000000000
χ808-88-88-8000-2−4i24i2−4i24i22-2200000000-2200000000000000000000000i2−i2i2−i200000000000000000000000000000
χ818-88-8-88000-242−42−42422-22000000002-200000000000000000000000−222−200000000000000000000000000000
χ828-88-8-88000-2−424242−422-22000000002-2000000000000000000000002−2−2200000000000000000000000000000
χ8316-16-161600000-4000044-4000000000000000000000000000000000000000000000000000000000000000000

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