Finite Group Databasebeta

← Group #13032053

Character table — Group #13032053

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size11112222444444444555588888888101010101010101010101010101010101616161616161616162020202020202020202020202020203232404040404040404040404040
order12224444458888101010444422442020202044448888888888881010202020404040402888888888888881020444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-111111111111111111111-1-11-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111-1-1-1-111111111-1-1-1-1iiiiii−i−i−i−i−i−i111111111-1-1-1-1-1i−iiiii−i−i−i−i11-1-1-1-1iiii−i−i−i−i
χ611111111111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−iiiiiii111111111-1-1-1-1-1−ii−i−i−i−iiiii11-1-1-1-1−i−i−i−iiiii
χ711111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−i-1-11-1-11111-1-1-1-1-1i−iiiii−i−i−i−i-1-11111−i−i−i−iiiii
χ811111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii-1-11-1-11111-1-1-1-1-1−ii−i−i−i−iiiii-1-11111iiii−i−i−i−i
χ91111111111-1-1-1-111111111-11-11111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ101111111111-1-1-1-111111111-11-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-111111111-1-11-11-1-1-111-1-111
χ111111111111-1-1-1-11111111-11-1111111111111111111111-1-11-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111-11-11-1-111-1-111
χ121111111111-1-1-1-11111111-11-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-11111111111-11-1111-1-111-1-1
χ131111111111-1-1-1-1111-1-1-1-11-11-11111-1-1-1-1iiiiii−i−i−i−i−i−i11111-1-1-1-1-11111i−i−i−i−i−iiiii-1-1-11-11ii−i−i−i−iii
χ141111111111-1-1-1-1111-1-1-1-11-11-11111-1-1-1-1−i−i−i−i−i−iiiiiii11111-1-1-1-1-11111−iiiiii−i−i−i−i-1-1-11-11−i−iiiii−i−i
χ151111111111-1-1-1-1111-1-1-1-1-11-111111-1-1-1-1iiiiii−i−i−i−i−i−i-1-11-1-1-1-1-1-1-11111i−i−i−i−i−iiiii111-11-1−i−iiiii−i−i
χ161111111111-1-1-1-1111-1-1-1-1-11-111111-1-1-1-1−i−i−i−i−i−iiiiiii-1-11-1-1-1-1-1-1-11111−iiiiii−i−i−i−i111-11-1ii−i−i−i−iii
χ171111-1-111-1111-1-1111111111-1-11-1-11-1-1111111-1-11111-1-111-1-1-111-1-1-111-1-1-1-111-1-111-1-11-1-1-1111-11-11-11-1
χ181111-1-111-1111-1-1111111111-1-11-1-11-1-111-1-1-1-111-1-1-1-11111-1-1-111-1-1-111-1-111-1-111-1-1111-1-1-111-11-11-11-11
χ191111-1-111-1111-1-11111111-1-1111-1-11-1-1111111-1-11111-1-1-1-1-11111-1-1-111-1-1-1-111-1-111-1-1-1111-1-1-11-11-11-11
χ201111-1-111-1111-1-11111111-1-1111-1-11-1-111-1-1-1-111-1-1-1-111-1-1-11111-1-1-111-1-111-1-111-1-111-1111-1-11-11-11-11-1
χ211111-1-111-1111-1-1111-1-1-1-111-1-11-1-1111-1-1iiii−i−i−i−i−i−iii11-1-1-111-1-11-1-111−iiii−i−i−i−iii1-111-1-1i−ii−i−ii−ii
χ221111-1-111-1111-1-1111-1-1-1-111-1-11-1-1111-1-1−i−i−i−iiiiiii−i−i11-1-1-111-1-11-1-111i−i−i−iiiii−i−i1-111-1-1−ii−iii−ii−i
χ231111-1-111-1111-1-1111-1-1-1-1-1-1111-1-1111-1-1iiii−i−i−i−i−i−iii-1-1-11111-1-11-1-111−iiii−i−i−i−iii-11-1-111−ii−iii−ii−i
χ241111-1-111-1111-1-1111-1-1-1-1-1-1111-1-1111-1-1−i−i−i−iiiiiii−i−i-1-1-11111-1-11-1-111i−i−i−iiiii−i−i-11-1-111i−ii−i−ii−ii
χ251111-1-111-11-1-11111111111-1-111-1-11-1-1111111-1-11111-1-111-1-1-1-1-111-1-1-111-1-1-1-111-1-111-11-111-11-1-111-1-11
χ261111-1-111-11-1-11111111111-1-111-1-11-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1111111-1-111-1-1-11-111-1-111-1-111-1
χ271111-1-111-11-1-1111111111-111-11-1-11-1-1111111-1-11111-1-1-1-1-111-1-111-1-1-111-1-1-1-111-1-1111-11-1-11-111-1-111-1
χ281111-1-111-11-1-1111111111-111-11-1-11-1-111-1-1-1-111-1-1-1-111-1-1-111-1-111-1-1-1111111-1-111-1-11-11-1-111-1-111-1-11
χ291111-1-111-11-1-111111-1-1-1-11-1-111-1-1111-1-1iiii−i−i−i−i−i−iii11-1-1-1-1-111111-1-1−ii−i−iiiii−i−i-111-1-11i−i−ii−iii−i
χ301111-1-111-11-1-111111-1-1-1-11-1-111-1-1111-1-1−i−i−i−iiiiiii−i−i11-1-1-1-1-111111-1-1i−iii−i−i−i−iii-111-1-11−iii−ii−i−ii
χ311111-1-111-11-1-111111-1-1-1-1-111-11-1-1111-1-1iiii−i−i−i−i−i−iii-1-1-111-1-111111-1-1−ii−i−iiiii−i−i1-1-111-1−iii−ii−i−ii
χ321111-1-111-11-1-111111-1-1-1-1-111-11-1-1111-1-1−i−i−i−iiiiiii−i−i-1-1-111-1-111111-1-1i−iii−i−i−i−iii1-1-111-1i−i−ii−iii−i
χ33222222-2-2-22000022222220000-222-222-2-222-2-22222-2-22200-2000000-20000-2-20000000000000000000000
χ34222222-2-2-22000022222220000-222-222-2-2-2-222-2-2-2-222-2-200-2000000-20000220000000000000000000000
χ35222222-2-2-220000222-2-2-2-20000-222-2-2-2222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00-200000020000−2i2i0000000000000000000000
χ36222222-2-2-220000222-2-2-2-20000-222-2-2-222−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00-2000000200002i−2i0000000000000000000000
χ372222-2-2-2-222000022222220000-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-200200000020000220000000000000000000000
χ382222-2-2-2-222000022222220000-2-2-2-2-2-2-2-2-2-22222-2-2222200200000020000-2-20000000000000000000000
χ392222-2-2-2-2220000222-2-2-2-20000-2-2-2-222222i2i−2i−2i−2i−2i−2i−2i2i2i2i2i002000000-200002i−2i0000000000000000000000
χ402222-2-2-2-2220000222-2-2-2-20000-2-2-2-22222−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i002000000-20000−2i2i0000000000000000000000
χ412-2-222i−2i00022−2i2−i22-2-222-2-2000002i−2i02i−2i002-2002i−2i2-2002i−2i000002−2i2−i202−2i2−i2002−2i2−i22−2i2−i200000000000000
χ422-2-222i−2i00022−2i2−i22-2-222-2-2000002i−2i02i−2i00-2200−2i2i-2200−2i2i000002−2i2−i202−2i2−i200−22−i2i2−22−i2i200000000000000
χ432-2-222i−2i00022−2i2−i22-2-2-2-222000002i−2i0−2i2i002i−2i00-22−2i2i002-2000002−2i2−i20−22−i2i200i2−i2−22−i2i22−200000000000000
χ442-2-222i−2i00022−2i2−i22-2-2-2-222000002i−2i0−2i2i00−2i2i002-22i−2i00-22000002−2i2−i20−22−i2i200−i2i22−2i2−i2−2200000000000000
χ452-2-222i−2i0002−22−i2i22-2-222-2-2000002i−2i02i−2i002-2002i−2i2-2002i−2i00000−22−i2i20−22−i2i200−22−i2i2−22−i2i200000000000000
χ462-2-222i−2i0002−22−i2i22-2-222-2-2000002i−2i02i−2i00-2200−2i2i-2200−2i2i00000−22−i2i20−22−i2i2002−2i2−i22−2i2−i200000000000000
χ472-2-222i−2i0002−22−i2i22-2-2-2-222000002i−2i0−2i2i002i−2i00-22−2i2i002-200000−22−i2i202−2i2−i200−i2i22−2i2−i2−2200000000000000
χ482-2-222i−2i0002−22−i2i22-2-2-2-222000002i−2i0−2i2i00−2i2i002-22i−2i00-2200000−22−i2i202−2i2−i200i2−i2−22−i2i22−200000000000000
χ492-2-22−2i2i00022−2−i2i22-2-222-2-200000−2i2i0−2i2i002-200−2i2i2-200−2i2i000002−2−i2i202−2−i2i2002−2−i2i22−2−i2i200000000000000
χ502-2-22−2i2i00022−2−i2i22-2-222-2-200000−2i2i0−2i2i00-22002i−2i-22002i−2i000002−2−i2i202−2−i2i200−22i2−i2−22i2−i200000000000000
χ512-2-22−2i2i00022−2−i2i22-2-2-2-22200000−2i2i02i−2i002i−2i002-2−2i2i00-22000002−2−i2i20−22i2−i200i2−i22−2−i2i2−2200000000000000
χ522-2-22−2i2i00022−2−i2i22-2-2-2-22200000−2i2i02i−2i00−2i2i00-222i−2i002-2000002−2−i2i20−22i2−i200−i2i2−22i2−i22−200000000000000
χ532-2-22−2i2i0002−22i2−i22-2-222-2-200000−2i2i0−2i2i002-200−2i2i2-200−2i2i00000−22i2−i20−22i2−i200−22i2−i2−22i2−i200000000000000
χ542-2-22−2i2i0002−22i2−i22-2-222-2-200000−2i2i0−2i2i00-22002i−2i-22002i−2i00000−22i2−i20−22i2−i2002−2−i2i22−2−i2i200000000000000
χ552-2-22−2i2i0002−22i2−i22-2-2-2-22200000−2i2i02i−2i002i−2i002-2−2i2i00-2200000−22i2−i202−2−i2i200−i2i2−22i2−i22−200000000000000
χ562-2-22−2i2i0002−22i2−i22-2-2-2-22200000−2i2i02i−2i00−2i2i00-222i−2i002-200000−22i2−i202−2−i2i200i2−i22−2−i2i2−2200000000000000
χ57444444444-14444-1-1-100004444-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1000000000000000-1-1000000000000
χ58444444444-14444-1-1-10000-4-4-4-4-1-1-1-1000000000000000011-111-1-1-1-100000000000000011000000000000
χ59444444444-1-4-4-4-4-1-1-100004-44-4-1-1-1-10000000000000000-1-1-1-1-1111100000000000000011000000000000
χ60444444444-1-4-4-4-4-1-1-10000-44-44-1-1-1-1000000000000000011-1111111000000000000000-1-1000000000000
χ614444-4-444-4-144-4-4-1-1-1000044-4-4-111-10000000000000000-1-1111-1-111000000000000000-11000000000000
χ624444-4-444-4-144-4-4-1-1-10000-4-444-111-10000000000000000111-1-1-1-1110000000000000001-1000000000000
χ634444-4-444-4-1-4-444-1-1-100004-4-44-111-10000000000000000-1-111111-1-10000000000000001-1000000000000
χ644444-4-444-4-1-4-444-1-1-10000-444-4-111-10000000000000000111-1-111-1-1000000000000000-11000000000000
χ6544-4-40000040000-44-44i−4i4i−4i00000000000000−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ390000−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ370000000000000000000000000000000000000000
χ6644-4-40000040000-44-44i−4i4i−4i000000000000004ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ3900004ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ370000000000000000000000000000000000000000
χ6744-4-40000040000-44-4−4i4i−4i4i00000000000000−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ370000−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ390000000000000000000000000000000000000000
χ6844-4-40000040000-44-4−4i4i−4i4i000000000000004ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ3700004ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ390000000000000000000000000000000000000000
χ694-44-4004-4040000-4-444i−4i−4i4i0000-4004004i−4i00000000000000000000000000000000000000000000000000
χ704-44-4004-4040000-4-44−4i4i4i−4i0000-400400−4i4i00000000000000000000000000000000000000000000000000
χ714-44-400-44040000-4-444i−4i−4i4i0000400-400−4i4i00000000000000000000000000000000000000000000000000
χ724-44-400-44040000-4-44−4i4i4i−4i0000400-4004i−4i00000000000000000000000000000000000000000000000000
χ73888888-8-8-8-20000-2-2-2000000002-2-22000000000000000000200000000000000000000000000000000000
χ748888-8-8-8-88-20000-2-2-2000000002222000000000000000000-200000000000000000000000000000000000
χ758-88-8008-80-2000022-200000000200-2000000000000000025−25000000000000000000000000000000000000
χ768-88-8008-80-2000022-200000000200-20000000000000000−2525000000000000000000000000000000000000
χ778-88-800-880-2000022-200000000-200200000000000000000002i5−2i5000000000000000000000000000000000
χ788-88-800-880-2000022-200000000-20020000000000000000000−2i52i5000000000000000000000000000000000
χ798-8-888i−8i000-242−424i2−4i2-222000000000−2i2i0000000000000000000000−22−i2i200000000000000000000000000000
χ808-8-888i−8i000-2−4242−4i24i2-222000000000−2i2i00000000000000000000002−2i2−i200000000000000000000000000000
χ818-8-88−8i8i000-242−42−4i24i2-2220000000002i−2i0000000000000000000000−22i2−i200000000000000000000000000000
χ828-8-88−8i8i000-2−42424i2−4i2-2220000000002i−2i00000000000000000000002−2−i2i200000000000000000000000000000
χ831616-16-1600000-400004-44000000000000000000000000000000000000000000000000000000000000000000

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