Finite Group Databasebeta

← Group #13017202

Character table — Group #13017202

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222244444444444445555555555558888881010101010101010101010101616161616161616162020202020202020202020202020202020202020202020202020203232404040404040
order12222244444445888810101044448888888844101020204444888888882020202020404040404444488888888888888888888882020448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1ii−i−iii−i−i111111111-1-1-1-1-1-1-1-1-1i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i
χ4111111111111111111111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−iii−i−iii111111111-1-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii
χ511111111111111-1-1-1-1111111111111111-1-1111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111-1-1-1-1111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1ii−i−iii−i−i11111-1-1-1-1-1-1-1-1-11111i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii
χ811111111111111-1-1-1-1111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−iii−i−iii11111-1-1-1-1-1-1-1-1-11111−iiiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i
χ9111111111-1-1-1-111111111111111111111-1-111111111111111111-1-1-1-111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ10111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ11111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1ii−i−iii−i−i1-1-1-1-11111-11111-1-1-1-1i−iiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii
χ12111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−iii−i−iii1-1-1-1-11111-11111-1-1-1-1−ii−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i
χ13111111111-1-1-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ14111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ15111111111-1-1-1-11-1-1-1-1111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1ii−i−iii−i−i1-1-1-1-1-1-1-1-1-111111111i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−i
χ16111111111-1-1-1-11-1-1-1-1111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−iii−i−iii1-1-1-1-1-1-1-1-1-111111111−iiiiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii
χ171111-1-1-1-11ii−i−i1ii−i−i1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11ii−i−iii−i−i1ii−i−iii−i−i11ii−i−iii−i−iii−i−iii−i−i-11-111-11-1
χ181111-1-1-1-11ii−i−i1ii−i−i1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111111ii−i−iii−i−i1ii−i−iii−i−i-1-1−i−iii−i−iii−i−iii−i−iii-11-11-11-11
χ191111-1-1-1-11ii−i−i1ii−i−i111-1-1-1-1iiii−i−i−i−i1-1-1-1-1-11111−i−iii−i−iii1ii−i−iii−i−i-1−i−iii−i−iiii−i-1-11111-1-1-1-11111-1-1-111-1i−i−ii
χ201111-1-1-1-11ii−i−i1ii−i−i111-1-1-1-1−i−i−i−iiiii1-1-1-1-1-11111ii−i−iii−i−i1ii−i−iii−i−i-1−i−iii−i−iii−ii11-1-1-1-11111-1-1-1-111-111-1−iii−i
χ211111-1-1-1-11ii−i−i1−i−iii111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11ii−i−i−i−iii1ii−i−i−i−iii11−i−iii−i−iiiii−i−iii−i−i1-11-1-11-11
χ221111-1-1-1-11ii−i−i1−i−iii1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111ii−i−i−i−iii1ii−i−i−i−iii-1-1ii−i−iii−i−i−i−iii−i−iii1-11-11-11-1
χ231111-1-1-1-11ii−i−i1−i−iii111-1-1-1-1iiii−i−i−i−i-11-1-1-1-11111−i−iii−i−iii1ii−i−i−i−iii-1−i−iiiii−i−ii−i11-1-1-1-111-1-11111-1-11-1-11−iii−i
χ241111-1-1-1-11ii−i−i1−i−iii111-1-1-1-1−i−i−i−iiiii-11-1-1-1-11111ii−i−iii−i−i1ii−i−i−i−iii-1−i−iiiii−i−i−ii-1-11111-1-111-1-1-1-1111-1-11i−i−ii
χ251111-1-1-1-11−i−iii1ii−i−i111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i−iiiii−i−i1−i−iiiii−i−i11ii−i−iii−i−i−i−iii−i−iii1-11-1-11-11
χ261111-1-1-1-11−i−iii1ii−i−i1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111−i−iiiii−i−i1−i−iiiii−i−i-1-1−i−iii−i−iiiii−i−iii−i−i1-11-11-11-1
χ271111-1-1-1-11−i−iii1ii−i−i111-1-1-1-1iiii−i−i−i−i-11-1-1-1-11111−i−iii−i−iii1−i−iiiii−i−i-1ii−i−i−i−iiii−i-1-11111-1-111-1-1-1-1111-1-11−iii−i
χ281111-1-1-1-11−i−iii1ii−i−i111-1-1-1-1−i−i−i−iiiii-11-1-1-1-11111ii−i−iii−i−i1−i−iiiii−i−i-1ii−i−i−i−iii−ii11-1-1-1-111-1-11111-1-11-1-11i−i−ii
χ291111-1-1-1-11−i−iii1−i−iii1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i−iii−i−iii1−i−iii−i−iii11−i−iii−i−iii−i−iii−i−iii-11-111-11-1
χ301111-1-1-1-11−i−iii1−i−iii1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111111−i−iii−i−iii1−i−iii−i−iii-1-1ii−i−iii−i−iii−i−iii−i−i-11-11-11-11
χ311111-1-1-1-11−i−iii1−i−iii111-1-1-1-1iiii−i−i−i−i1-1-1-1-1-11111−i−iii−i−iii1−i−iii−i−iii-1ii−i−iii−i−ii−i11-1-1-1-11111-1-1-1-111-111-1i−i−ii
χ321111-1-1-1-11−i−iii1−i−iii111-1-1-1-1−i−i−i−iiiii1-1-1-1-1-11111ii−i−iii−i−i1−i−iii−i−iii-1ii−i−iii−i−i−ii-1-11111-1-1-1-11111-1-1-111-1−iii−i
χ33222222-2-2-20000200002222222222222220022-2-22-2-222222-2-2-2-2-200000000-200000000-2-2000000000000000000000000
χ34222222-2-2-20000200002222222-2-2-2-2-2-2-2-20022-2-22-2-22-2-2-2-22222-200000000-20000000022000000000000000000000000
χ35222222-2-2-2000020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i0022-2-2-222-22i2i−2i−2i−2i−2i2i2i-200000000200000000−2i2i000000000000000000000000
χ36222222-2-2-2000020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i0022-2-2-222-2−2i−2i2i2i2i2i−2i−2i-2000000002000000002i−2i000000000000000000000000
χ372222-2-222-200002000022222222222222200-2-222-222-2-2-2-2-22222-200000000-200000000-2-2000000000000000000000000
χ382222-2-222-20000200002222222-2-2-2-2-2-2-2-200-2-222-222-22222-2-2-2-2-200000000-20000000022000000000000000000000000
χ392222-2-222-2000020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-2-2222-2-22−2i−2i2i2i2i2i−2i−2i-200000000200000000−2i2i000000000000000000000000
χ402222-2-222-2000020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-2-2222-2-222i2i−2i−2i−2i−2i2i2i-2000000002000000002i−2i000000000000000000000000
χ4122-2-22-2000000022−22−22-2-222-2-222-2-222-2-2002-200200-22-22-20000000002−22−2000002−22−2002−22−22−22−20000000000000000
χ4222-2-22-2000000022−22−22-2-222-2-2-2-222-2-222002-200200-2-22-220000000002−22−2000002−22−200−22−22−22−220000000000000000
χ4322-2-22-2000000022−22−22-2-2-2-2222i2i−2i−2i−2i−2i2i2i002-200-20022i−2i−2i2i0000000002−22−200000−22−2200i2−i2i2−i2−i2i2−i2i20000000000000000
χ4422-2-22-2000000022−22−22-2-2-2-222−2i−2i2i2i2i2i−2i−2i002-200-2002−2i2i2i−2i0000000002−22−200000−22−2200−i2i2−i2i2i2−i2i2−i20000000000000000
χ4522-2-22-200000002−22−222-2-222-2-222-2-222-2-2002-200200-22-22-2000000000−22−2200000−22−2200−22−22−22−220000000000000000
χ4622-2-22-200000002−22−222-2-222-2-2-2-222-2-222002-200200-2-22-22000000000−22−2200000−22−22002−22−22−22−20000000000000000
χ4722-2-22-200000002−22−222-2-2-2-2222i2i−2i−2i−2i−2i2i2i002-200-20022i−2i−2i2i000000000−22−22000002−22−200−i2i2−i2i2i2−i2i2−i20000000000000000
χ4822-2-22-200000002−22−222-2-2-2-222−2i−2i2i2i2i2i−2i−2i002-200-2002−2i2i2i−2i000000000−22−22000002−22−200i2−i2i2−i2−i2i2−i2i20000000000000000
χ4922-2-2-2200000002i2−i2−i2i22-2-222-2-222-2-222-2-200-2200-2002-22-22000000000i2−i2−i2i200000i2−i2−i2i200i2−i2−i2i2i2−i2−i2i20000000000000000
χ5022-2-2-2200000002i2−i2−i2i22-2-222-2-2-2-222-2-22200-2200-20022-22-2000000000i2−i2−i2i200000i2−i2−i2i200−i2i2i2−i2−i2i2i2−i20000000000000000
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χ5622-2-2-2200000002−i2i2i2−i22-2-2-2-222−2i−2i2i2i2i2i−2i−2i00-2200200-22i−2i−2i2i000000000−i2i2i2−i200000i2−i2−i2i200−222−22−2−220000000000000000
χ572-2-22002i−2i01+i−1−i1−i−1+i20000-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300002i−2i02-2000002ζ3−2ζ32ζ−2ζ01+i−1−i1−i−1+i000001−i−1+i1+i−1−i00000000000000i2−i22−22−2i2−i200000000
χ582-2-22002i−2i01+i−1−i1−i−1+i20000-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300002i−2i02-200000−2ζ32ζ3−2ζ2ζ01+i−1−i1−i−1+i000001−i−1+i1+i−1−i00000000000000−i2i2−22−22−i2i200000000
χ592-2-22002i−2i01+i−1−i1−i−1+i20000-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00002i−2i0-2200000−2ζ2ζ−2ζ32ζ301+i−1−i1−i−1+i00000−1+i1−i−1−i1+i00000000000000−22i2−i2−i2i22−200000000
χ602-2-22002i−2i01+i−1−i1−i−1+i20000-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00002i−2i0-22000002ζ−2ζ2ζ3−2ζ301+i−1−i1−i−1+i00000−1+i1−i−1−i1+i000000000000002−2−i2i2i2−i2−2200000000
χ612-2-22002i−2i0−1−i1+i−1+i1−i20000-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300002i−2i02-2000002ζ3−2ζ32ζ−2ζ0−1−i1+i−1+i1−i00000−1+i1−i−1−i1+i00000000000000−i2i2−22−22−i2i200000000
χ622-2-22002i−2i0−1−i1+i−1+i1−i20000-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300002i−2i02-200000−2ζ32ζ3−2ζ2ζ0−1−i1+i−1+i1−i00000−1+i1−i−1−i1+i00000000000000i2−i22−22−2i2−i200000000
χ632-2-22002i−2i0−1−i1+i−1+i1−i20000-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00002i−2i0-2200000−2ζ2ζ−2ζ32ζ30−1−i1+i−1+i1−i000001−i−1+i1+i−1−i000000000000002−2−i2i2i2−i2−2200000000
χ642-2-22002i−2i0−1−i1+i−1+i1−i20000-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00002i−2i0-22000002ζ−2ζ2ζ3−2ζ30−1−i1+i−1+i1−i000001−i−1+i1+i−1−i00000000000000−22i2−i2−i2i22−200000000
χ652-2-2200−2i2i01−i−1+i1+i−1−i20000-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000−2i2i0-2200000−2ζ32ζ3−2ζ2ζ01−i−1+i1+i−1−i00000−1−i1+i−1+i1−i000000000000002−2i2−i2−i2i2−2200000000
χ662-2-2200−2i2i01−i−1+i1+i−1−i20000-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000−2i2i0-22000002ζ3−2ζ32ζ−2ζ01−i−1+i1+i−1−i00000−1−i1+i−1+i1−i00000000000000−22−i2i2i2−i22−200000000
χ672-2-2200−2i2i01−i−1+i1+i−1−i20000-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000−2i2i02-2000002ζ−2ζ2ζ3−2ζ301−i−1+i1+i−1−i000001+i−1−i1−i−1+i00000000000000i2−i2−22−22i2−i200000000
χ682-2-2200−2i2i01−i−1+i1+i−1−i20000-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000−2i2i02-200000−2ζ2ζ−2ζ32ζ301−i−1+i1+i−1−i000001+i−1−i1−i−1+i00000000000000−i2i22−22−2−i2i200000000
χ692-2-2200−2i2i0−1+i1−i−1−i1+i20000-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000−2i2i0-2200000−2ζ32ζ3−2ζ2ζ0−1+i1−i−1−i1+i000001+i−1−i1−i−1+i00000000000000−22−i2i2i2−i22−200000000
χ702-2-2200−2i2i0−1+i1−i−1−i1+i20000-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000−2i2i0-22000002ζ3−2ζ32ζ−2ζ0−1+i1−i−1−i1+i000001+i−1−i1−i−1+i000000000000002−2i2−i2−i2i2−2200000000
χ712-2-2200−2i2i0−1+i1−i−1−i1+i20000-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000−2i2i02-2000002ζ−2ζ2ζ3−2ζ30−1+i1−i−1−i1+i00000−1−i1+i−1+i1−i00000000000000−i2i22−22−2−i2i200000000
χ722-2-2200−2i2i0−1+i1−i−1−i1+i20000-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000−2i2i02-200000−2ζ2ζ−2ζ32ζ30−1+i1−i−1−i1+i00000−1−i1+i−1+i1−i00000000000000i2−i2−22−22i2−i200000000
χ734444444444444-14444-1-1-100000000000044-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1000000000000000000000000000-1-1000000
χ744444444444444-1-4-4-4-4-1-1-1000000000000-4-4-1-1-1-1000000000000-1-1-1-1-1111100000000000000000000000000011000000
χ75444444444-4-4-4-4-14444-1-1-1000000000000-4-4-1-1-1-1000000000000-11111-1-1-1-100000000000000000000000000011000000
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χ804444-4-4-4-44−4i−4i4i4i-1−4i−4i4i4i-1-1-10000000000004-41111000000000000-1ii−i−iii−i−i0000000000000000000000000001-1000000
χ814-44-400000000040000-4-444i−4i−4i4i4ζ−4ζ−4ζ4ζ4ζ3−4ζ3−4ζ34ζ300000000000000000000000000000000000000000000000000000000000000
χ824-44-400000000040000-4-444i−4i−4i4i−4ζ4ζ4ζ−4ζ−4ζ34ζ34ζ3−4ζ300000000000000000000000000000000000000000000000000000000000000
χ834-44-400000000040000-4-44−4i4i4i−4i4ζ3−4ζ3−4ζ34ζ34ζ−4ζ−4ζ4ζ00000000000000000000000000000000000000000000000000000000000000
χ844-44-400000000040000-4-44−4i4i4i−4i−4ζ34ζ34ζ3−4ζ3−4ζ4ζ4ζ−4ζ00000000000000000000000000000000000000000000000000000000000000
χ85888888-8-8-80000-20000-2-2-200000000000000-2-22200000000000020000000000000000000000000000000000000000000
χ868888-8-888-80000-20000-2-2-20000000000000022-2-200000000000020000000000000000000000000000000000000000000
χ8788-8-88-80000000-242−4242−42-22200000000000000-220000000000000000000−22−2200000000000000000000000000000000000
χ8888-8-88-80000000-2−4242−4242-22200000000000000-2200000000000000000002−22−200000000000000000000000000000000000
χ8988-8-8-880000000-24i2−4i2−4i24i2-222000000000000002-20000000000000000000−i2i2i2−i200000000000000000000000000000000000
χ9088-8-8-880000000-2−4i24i24i2−4i2-222000000000000002-20000000000000000000i2−i2−i2i200000000000000000000000000000000000
χ918-8-88008i−8i04+4i−4−4i4−4i−4+4i-200002-220000000000000000−2i2i0000000000000−1−i1+i−1+i1−i000000000000000000000000000000000000000
χ928-8-88008i−8i0−4−4i4+4i−4+4i4−4i-200002-220000000000000000−2i2i00000000000001+i−1−i1−i−1+i000000000000000000000000000000000000000
χ938-8-8800−8i8i04−4i−4+4i4+4i−4−4i-200002-2200000000000000002i−2i0000000000000−1+i1−i−1−i1+i000000000000000000000000000000000000000
χ948-8-8800−8i8i0−4+4i4−4i−4−4i4+4i-200002-2200000000000000002i−2i00000000000001−i−1+i1+i−1−i000000000000000000000000000000000000000
χ9516-1616-16000000000-4000044-400000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.