Finite Group Databasebeta

← Group #13052033

Character table — Group #13052033

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444444666666667777777712121212121212121212121214141414282828282828282828282828565656565656565656565656
order12224424888871414142828282833666666141428285656565656565656121212126612122424242424242424244466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ411111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32
χ511111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ611111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32
χ711111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1111-1-11-1-1
χ811111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-111-111
χ911111111-1-1-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321-11-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ1011111111-1-1-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-11-111+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ1111111111-1-1-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321-11-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ1211111111-1-1-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-11-111−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ13111111-1-111-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-11-1-11-1
χ14111111-1-111-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-11-111-11
χ15111111-1-111-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ16111111-1-111-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1111+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ17111111-1-111-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ18111111-1-111-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1111−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ19111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1-1111-1-11-1-11
χ20111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-111-1-1-111-111-1
χ21111111-1-1-1-11111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ22111111-1-1-1-11111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111-11+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ23111111-1-1-1-11111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ24111111-1-1-1-11111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111-11−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ252222-2-22-200002222-2-2-2-22222222222-2-200000000-2-2-2-222-2-200000000000000000000
χ262222-2-22-200002222-2-2-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322-2-2000000001+i31−i31+i31−i3−1−i3−1+i31+i31−i300000000000000000000
χ272222-2-22-200002222-2-2-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322-2-2000000001−i31+i31−i31+i3−1+i3−1−i31−i31+i300000000000000000000
χ282222-2-2-2200002222-2-2-2-222222222-2-22200000000-2-2-2-2-2-22200000000000000000000
χ292222-2-2-2200002222-2-2-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-222000000001+i31−i31+i31−i31+i31−i3−1−i3−1+i300000000000000000000
χ302222-2-2-2200002222-2-2-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-222000000001−i31+i31−i31+i31−i31+i3−1+i3−1−i300000000000000000000
χ312-22-22-200002i−2i2-2-2222-2-222-2-22-22-2000000002i2i−2i−2i22-2-20000002i−2i002i−2i000000000000
χ322-22-22-200002i−2i2-2-2222-2-2−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i3000000002i2i−2i−2i−1−i3−1+i31+i31−i30000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79000000000000
χ332-22-22-200002i−2i2-2-2222-2-2−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i3000000002i2i−2i−2i−1+i3−1−i31−i31+i30000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83000000000000
χ342-22-22-20000−2i2i2-2-2222-2-222-2-22-22-200000000−2i−2i2i2i22-2-2000000−2i2i00−2i2i000000000000
χ352-22-22-20000−2i2i2-2-2222-2-2−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i300000000−2i−2i2i2i−1−i3−1+i31+i31−i3000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79000000000000
χ362-22-22-20000−2i2i2-2-2222-2-2−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i300000000−2i−2i2i2i−1+i3−1−i31−i31+i3000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83000000000000
χ372-22-2-22002-2002-2-22-2-22222-2-22-22-2000022-2-20000-2-22200002-2002-200000000000000
χ382-22-2-22002-2002-2-22-2-222−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i3000022-2-200001+i31−i3−1−i3−1+i30000−1−i31+i300−1+i31−i300000000000000
χ392-22-2-22002-2002-2-22-2-222−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i3000022-2-200001−i31+i3−1+i3−1−i30000−1+i31−i300−1−i31+i300000000000000
χ402-22-2-2200-22002-2-22-2-22222-2-22-22-20000-2-2220000-2-2220000-2200-2200000000000000
χ412-22-2-2200-22002-2-22-2-222−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000-2-22200001+i31−i3−1−i3−1+i300001+i3−1−i3001−i3−1+i300000000000000
χ422-22-2-2200-22002-2-22-2-222−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000-2-22200001−i31+i3−1+i3−1−i300001−i3−1+i3001+i3−1−i300000000000000
χ4344-4-40000000044-4-400004444-4-4-4-40000000000000000000000000000000000000000
χ4444-4-40000000044-4-40000−2−2i3−2+2i3−2−2i3−2+2i32+2i32+2i32−2i32−2i30000000000000000000000000000000000000000
χ4544-4-40000000044-4-40000−2+2i3−2−2i3−2+2i3−2−2i32−2i32−2i32+2i32+2i30000000000000000000000000000000000000000
χ464-4-44000000004-44-4000044-4-4-44-440000000000000000000000000000000000000000
χ474-4-44000000004-44-40000−2−2i3−2+2i32+2i32−2i32+2i3−2−2i32−2i3−2+2i30000000000000000000000000000000000000000
χ484-4-44000000004-44-40000−2+2i3−2−2i32−2i32+2i32−2i3−2+2i32+2i3−2−2i30000000000000000000000000000000000000000
χ49666666666666-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ5066666666-6-6-6-6-1-1-1-1-1-1-1-100000000-1-1-1-1111111110000000000000000000000000000
χ51666666-6-666-6-6-1-1-1-1-1-1-1-1000000001111-1-1-1-111110000000000000000000000000000
χ52666666-6-6-6-666-1-1-1-1-1-1-1-10000000011111111-1-1-1-10000000000000000000000000000
χ536666-6-66-60000-1-1-1-1111100000000-1-1117−77−77−77−70000000000000000000000000000
χ546666-6-66-60000-1-1-1-1111100000000-1-111−77−77−77−770000000000000000000000000000
χ556666-6-6-660000-1-1-1-111110000000011-1-17−77−7−77−770000000000000000000000000000
χ566666-6-6-660000-1-1-1-111110000000011-1-1−77−777−77−70000000000000000000000000000
χ576-66-66-600006i−6i-111-1-1-11100000000−i7i7−i7i77−7−77−i−iii0000000000000000000000000000
χ586-66-66-600006i−6i-111-1-1-11100000000i7−i7i7−i7−777−7−i−iii0000000000000000000000000000
χ596-66-66-60000−6i6i-111-1-1-11100000000−i7i7−i7i7−777−7ii−i−i0000000000000000000000000000
χ606-66-66-60000−6i6i-111-1-1-11100000000i7−i7i7−i77−7−77ii−i−i0000000000000000000000000000
χ616-66-6-66006-600-111-111-1-100000000−i7i7i7−i7-1-111−i7i7i7−i70000000000000000000000000000
χ626-66-6-66006-600-111-111-1-100000000i7−i7−i7i7-1-111i7−i7−i7i70000000000000000000000000000
χ636-66-6-6600-6600-111-111-1-100000000−i7i7i7−i711-1-1i7−i7−i7i70000000000000000000000000000
χ646-66-6-6600-6600-111-111-1-100000000i7−i7−i7i711-1-1−i7i7i7−i70000000000000000000000000000
χ651212-12-1200000000-2-22227−2727−27000000000000000000000000000000000000000000000000
χ661212-12-1200000000-2-222−2727−2727000000000000000000000000000000000000000000000000
χ6712-12-121200000000-22-2227−27−2727000000000000000000000000000000000000000000000000
χ6812-12-121200000000-22-22−272727−27000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.