Finite Group Databasebeta

← Group #13017197

Character table — Group #13017197

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222244444444444445555555555558888881010101010101010101010101616161616161616162020202020202020202020202020202020202020202020202020203232404040404040
order12222244444445888810101044448888888824101020204444888888882020202020404040404444488888888888888888888881020248888
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−i1-1-111-11-1
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−iii1-1-11-11-11
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-1-11111-1-1-1-11111-1-11-11-1i−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−ii11-1-1-1-11111-1-1-1-1111-11-1−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−i-111-1-11-11
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−iii-111-11-11-1
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−i11-1-1-1-111-1-11111-1-1-11-11−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-1-11111-1-111-1-1-1-111-11-11i−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−iii-111-1-11-11
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−i-111-11-11-1
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-1-11111-1-111-1-1-1-111-11-11−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−ii11-1-1-1-111-1-11111-1-1-11-11i−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−iii1-1-111-11-1
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−i1-1-11-11-11
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−i11-1-1-1-11111-1-1-1-1111-11-1i−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-1-11111-1-1-1-11111-1-11-11-1−iii−i
χ33222222-2-2-20000200002222222222222220022-2-22-2-22-2-2-2-22222-200000000-200000000-2-2000000000000000000000000
χ34222222-2-2-20000200002222222-2-2-2-2-2-2-2-20022-2-22-2-222222-2-2-2-2-200000000-20000000022000000000000000000000000
χ35222222-2-2-2000020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i0022-2-2-222-2−2i−2i2i2i2i2i−2i−2i-200000000200000000−2i2i000000000000000000000000
χ36222222-2-2-2000020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i0022-2-2-222-22i2i−2i−2i−2i−2i2i2i-2000000002000000002i−2i000000000000000000000000
χ372222-2-222-200002000022222222222222200-2-222-222-22222-2-2-2-2-200000000-200000000-2-2000000000000000000000000
χ382222-2-222-20000200002222222-2-2-2-2-2-2-2-200-2-222-222-2-2-2-2-22222-200000000-20000000022000000000000000000000000
χ392222-2-222-2000020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-2-2222-2-222i2i−2i−2i−2i−2i2i2i-200000000200000000−2i2i000000000000000000000000
χ402222-2-222-2000020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-2-2222-2-22−2i−2i2i2i2i2i−2i−2i-2000000002000000002i−2i000000000000000000000000
χ412-22-2002i−2i01+i−1−i1−i−1+i200002-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300002i−2i02-202ζ3−2ζ32ζ−2ζ000001+i−1−i1−i−1+i000001−i−1+i1+i−1−i00000000000000i2−i22−22−2i2−i200000000
χ422-22-2002i−2i01+i−1−i1−i−1+i200002-2-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300002i−2i02-20−2ζ32ζ3−2ζ2ζ000001+i−1−i1−i−1+i000001−i−1+i1+i−1−i00000000000000−i2i2−22−22−i2i200000000
χ432-22-2002i−2i01+i−1−i1−i−1+i200002-2-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00002i−2i0-220−2ζ2ζ−2ζ32ζ3000001+i−1−i1−i−1+i00000−1+i1−i−1−i1+i00000000000000−22i2−i2−i2i22−200000000
χ442-22-2002i−2i01+i−1−i1−i−1+i200002-2-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00002i−2i0-2202ζ−2ζ2ζ3−2ζ3000001+i−1−i1−i−1+i00000−1+i1−i−1−i1+i000000000000002−2−i2i2i2−i2−2200000000
χ452-22-2002i−2i0−1−i1+i−1+i1−i200002-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300002i−2i02-202ζ3−2ζ32ζ−2ζ00000−1−i1+i−1+i1−i00000−1+i1−i−1−i1+i00000000000000−i2i2−22−22−i2i200000000
χ462-22-2002i−2i0−1−i1+i−1+i1−i200002-2-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300002i−2i02-20−2ζ32ζ3−2ζ2ζ00000−1−i1+i−1+i1−i00000−1+i1−i−1−i1+i00000000000000i2−i22−22−2i2−i200000000
χ472-22-2002i−2i0−1−i1+i−1+i1−i200002-2-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00002i−2i0-220−2ζ2ζ−2ζ32ζ300000−1−i1+i−1+i1−i000001−i−1+i1+i−1−i000000000000002−2−i2i2i2−i2−2200000000
χ482-22-2002i−2i0−1−i1+i−1+i1−i200002-2-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00002i−2i0-2202ζ−2ζ2ζ3−2ζ300000−1−i1+i−1+i1−i000001−i−1+i1+i−1−i00000000000000−22i2−i2−i2i22−200000000
χ492-22-200−2i2i01−i−1+i1+i−1−i200002-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000−2i2i0-220−2ζ32ζ3−2ζ2ζ000001−i−1+i1+i−1−i00000−1−i1+i−1+i1−i000000000000002−2i2−i2−i2i2−2200000000
χ502-22-200−2i2i01−i−1+i1+i−1−i200002-2-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000−2i2i0-2202ζ3−2ζ32ζ−2ζ000001−i−1+i1+i−1−i00000−1−i1+i−1+i1−i00000000000000−22−i2i2i2−i22−200000000
χ512-22-200−2i2i01−i−1+i1+i−1−i200002-2-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000−2i2i02-202ζ−2ζ2ζ3−2ζ3000001−i−1+i1+i−1−i000001+i−1−i1−i−1+i00000000000000i2−i2−22−22i2−i200000000
χ522-22-200−2i2i01−i−1+i1+i−1−i200002-2-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000−2i2i02-20−2ζ2ζ−2ζ32ζ3000001−i−1+i1+i−1−i000001+i−1−i1−i−1+i00000000000000−i2i22−22−2−i2i200000000
χ532-22-200−2i2i0−1+i1−i−1−i1+i200002-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000−2i2i0-220−2ζ32ζ3−2ζ2ζ00000−1+i1−i−1−i1+i000001+i−1−i1−i−1+i00000000000000−22−i2i2i2−i22−200000000
χ542-22-200−2i2i0−1+i1−i−1−i1+i200002-2-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000−2i2i0-2202ζ3−2ζ32ζ−2ζ00000−1+i1−i−1−i1+i000001+i−1−i1−i−1+i000000000000002−2i2−i2−i2i2−2200000000
χ552-22-200−2i2i0−1+i1−i−1−i1+i200002-2-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000−2i2i02-202ζ−2ζ2ζ3−2ζ300000−1+i1−i−1−i1+i00000−1−i1+i−1+i1−i00000000000000−i2i22−22−2−i2i200000000
χ562-22-200−2i2i0−1+i1−i−1−i1+i200002-2-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000−2i2i02-20−2ζ2ζ−2ζ32ζ300000−1+i1−i−1−i1+i00000−1−i1+i−1+i1−i00000000000000i2−i2−22−22i2−i200000000
χ572-2-222-200000002i2−i2i2−i2-22-222-2-22i−2i2i−2i2i−2i2i−2i002-200-200200002i−2i2i−2i00000i2−i2i2−i200000i2−i2i2−i2002−22−22−22−20000000000000000
χ582-2-222-200000002i2−i2i2−i2-22-222-2-2−2i2i−2i2i−2i2i−2i2i002-200-20020000−2i2i−2i2i00000i2−i2i2−i200000i2−i2i2−i200−22−22−22−220000000000000000
χ592-2-222-200000002i2−i2i2−i2-22-2-2-2222-22-2-22-22002-200200-200002-2-2200000i2−i2i2−i200000−i2i2−i2i200−i2i2−i2i2i2−i2i2−i20000000000000000
χ602-2-222-200000002i2−i2i2−i2-22-2-2-222-22-222-22-2002-200200-20000-222-200000i2−i2i2−i200000−i2i2−i2i200i2−i2i2−i2−i2i2−i2i20000000000000000
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χ632-2-222-200000002−i2i2−i2i2-22-2-2-2222-22-2-22-22002-200200-200002-2-2200000−i2i2−i2i200000i2−i2i2−i200i2−i2i2−i2−i2i2−i2i20000000000000000
χ642-2-222-200000002−i2i2−i2i2-22-2-2-222-22-222-22-2002-200200-20000-222-200000−i2i2−i2i200000i2−i2i2−i200−i2i2−i2i2i2−i2i2−i20000000000000000
χ652-2-22-22000000022−2−22-22-222-2-22i−2i2i−2i2i−2i2i−2i00-2200200-20000−2i2i−2i2i000002−2−22000002−2−2200−i2i2i2−i2−i2i2i2−i20000000000000000
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χ672-2-22-22000000022−2−22-22-2-2-2222-22-2-22-2200-2200-20020000-222-2000002−2−2200000−222−200−222−22−2−220000000000000000
χ682-2-22-22000000022−2−22-22-2-2-222-22-222-22-200-2200-200200002-2-22000002−2−2200000−222−2002−2−22−222−20000000000000000
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χ712-2-22-2200000002−222−2-22-2-2-2222-22-2-22-2200-2200-20020000-222-200000−222−2000002−2−22002−2−22−222−20000000000000000
χ722-2-22-2200000002−222−2-22-2-2-222-22-222-22-200-2200-200200002-2-2200000−222−2000002−2−2200−222−22−2−220000000000000000
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χ8144-4-400000000040000-4-444i−4i−4i4i4ζ3−4ζ3−4ζ34ζ3−4ζ4ζ4ζ−4ζ00000000000000000000000000000000000000000000000000000000000000
χ8244-4-400000000040000-4-444i−4i−4i4i−4ζ34ζ34ζ3−4ζ34ζ−4ζ−4ζ4ζ00000000000000000000000000000000000000000000000000000000000000
χ8344-4-400000000040000-4-44−4i4i4i−4i4ζ−4ζ−4ζ4ζ−4ζ34ζ34ζ3−4ζ300000000000000000000000000000000000000000000000000000000000000
χ8444-4-400000000040000-4-44−4i4i4i−4i−4ζ4ζ4ζ−4ζ4ζ3−4ζ3−4ζ34ζ300000000000000000000000000000000000000000000000000000000000000
χ85888888-8-8-80000-20000-2-2-200000000000000-2-22200000000000020000000000000000000000000000000000000000000
χ868888-8-888-80000-20000-2-2-20000000000000022-2-200000000000020000000000000000000000000000000000000000000
χ878-88-8008i−8i04+4i−4−4i4−4i−4+4i-20000-2220000000000000000−2i2i0000000000000−1−i1+i−1+i1−i000000000000000000000000000000000000000
χ888-88-8008i−8i0−4−4i4+4i−4+4i4−4i-20000-2220000000000000000−2i2i00000000000001+i−1−i1−i−1+i000000000000000000000000000000000000000
χ898-88-800−8i8i04−4i−4+4i4+4i−4−4i-20000-22200000000000000002i−2i0000000000000−1+i1−i−1−i1+i000000000000000000000000000000000000000
χ908-88-800−8i8i0−4+4i4−4i−4−4i4+4i-20000-22200000000000000002i−2i00000000000001−i−1+i1+i−1−i000000000000000000000000000000000000000
χ918-8-888-80000000-24i2−4i24i2−4i22-2200000000000000-220000000000000000000−i2i2−i2i200000000000000000000000000000000000
χ928-8-888-80000000-2−4i24i2−4i24i22-2200000000000000-220000000000000000000i2−i2i2−i200000000000000000000000000000000000
χ938-8-88-880000000-242−42−42422-22000000000000002-20000000000000000000−222−200000000000000000000000000000000000
χ948-8-88-880000000-2−424242−422-22000000000000002-200000000000000000002−2−2200000000000000000000000000000000000
χ951616-16-16000000000-4000044-400000000000000000000000000000000000000000000000000000000000000000000000000

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