Finite Group Databasebeta

← Group #13051991

Character table — Group #13051991

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122446666777777778812121212121214141414242424242828282828282828282828282828282856565656565656565656
order1222444471414143366666644282828282828121212122828282888881212121224242424242424242466121212121212
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111-1-11111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ5111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ6111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i321111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32
χ7111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1111111−1−i32−1−i32−1+i32−1+i32-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i321+i321+i321−i321−i32
χ8111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1111111−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ9111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ10111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i321111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32
χ11111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1111111−1+i32−1+i32−1−i32−1−i32-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i321−i321−i321+i321+i32
χ12111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1111111−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ13111111-1-11111111111111-111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-111-1-11-111-1-11-11-1
χ14111111-1-11111111111111-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-111-11-1-1111-11-1
χ15111111-1-1111111111111-1111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111-1-1-11-1-111-11-11
χ16111111-1-1111111111111-1111-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-1-1111-111-1-1-11-11
χ17111111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-111-1-1-1-1−1−i32−1−i32−1+i32−1+i3211-1-111-1-11+i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i32
χ18111111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-111-1-1-1-1−1−i32−1−i32−1+i32−1+i3211-1-1-1-1111+i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32
χ19111111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1111-1-1-1-1−1−i32−1−i32−1+i32−1+i32-1-11111-1-11+i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-111+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i32
χ20111111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1111-1-1-1-1−1−i32−1−i32−1+i32−1+i32-1-111-1-1111+i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1−1−i32−1+i321+i321−i321+i32−1−i321−i32−1+i32
χ21111111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-111-1-1-1-1−1+i32−1+i32−1−i32−1−i3211-1-111-1-11−i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i32
χ22111111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-111-1-1-1-1−1+i32−1+i32−1−i32−1−i3211-1-1-1-1111−i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32
χ23111111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1111-1-1-1-1−1+i32−1+i32−1−i32−1−i32-1-11111-1-11−i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-111−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i32
χ24111111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1111-1-1-1-1−1+i32−1+i32−1−i32−1−i32-1-111-1-1111−i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1−1+i32−1−i321−i321+i321−i32−1+i321+i32−1−i32
χ252222-2-22-222222222222200-2-222-2-2-2-2-2-20000000022-2-2000000000000000000
χ262222-2-22-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i300-2-222-2-21+i31+i31−i31−i300000000−1−i3−1+i31+i31−i3000000000000000000
χ272222-2-22-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i300-2-222-2-21−i31−i31+i31+i300000000−1+i3−1−i31−i31+i3000000000000000000
χ282222-2-2-2222222222222200-2-2-2-222-2-2-2-200000000-2-222000000000000000000
χ292222-2-2-222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i300-2-2-2-2221+i31+i31−i31−i3000000001+i31−i3−1−i3−1+i3000000000000000000
χ302222-2-2-222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i300-2-2-2-2221−i31−i31+i31+i3000000001−i31+i3−1+i3−1−i3000000000000000000
χ312-2-222-20022-2-222-2-222-2-2002-200002-22-20000002i−2i0000002i−2i002i−2i0000000000
χ322-2-222-20022-2-222-2-222-2-2002-200002-22-2000000−2i2i000000−2i2i00−2i2i0000000000
χ332-2-222-20022-2-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3002-20000−1−i31+i3−1+i31−i30000002i−2i0000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ790000000000
χ342-2-222-20022-2-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3002-20000−1−i31+i3−1+i31−i3000000−2i2i000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ790000000000
χ352-2-222-20022-2-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i3002-20000−1+i31−i3−1−i31+i30000002i−2i0000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ830000000000
χ362-2-222-20022-2-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i3002-20000−1+i31−i3−1−i31+i3000000−2i2i000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ830000000000
χ372-2-22-220022-2-222-2-222-2-200-220000-22-2200002i−2i0000002i−2i002i−2i000000000000
χ382-2-22-220022-2-222-2-222-2-200-220000-22-220000−2i2i000000−2i2i00−2i2i000000000000
χ392-2-22-220022-2-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i300-2200001+i3−1−i31−i3−1+i300002i−2i0000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79000000000000
χ402-2-22-220022-2-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i300-2200001+i3−1−i31−i3−1+i30000−2i2i000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79000000000000
χ412-2-22-220022-2-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i300-2200001−i3−1+i31+i3−1−i300002i−2i0000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83000000000000
χ422-2-22-220022-2-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i300-2200001−i3−1+i31+i3−1−i30000−2i2i000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83000000000000
χ4344-4-400004-44-44444-4-4-4-4000000000000000000000000000000000000000000
χ4444-4-400004-44-4−2−2i3−2+2i3−2−2i3−2+2i32+2i32−2i32+2i32−2i3000000000000000000000000000000000000000000
χ4544-4-400004-44-4−2+2i3−2−2i3−2+2i3−2−2i32−2i32+2i32−2i32+2i3000000000000000000000000000000000000000000
χ464-44-400004-4-4444-4-4-4-444000000000000000000000000000000000000000000
χ474-44-400004-4-44−2−2i3−2+2i32+2i32−2i32+2i32−2i3−2−2i3−2+2i3000000000000000000000000000000000000000000
χ484-44-400004-4-44−2+2i3−2−2i32−2i32+2i32−2i32+2i3−2+2i3−2−2i3000000000000000000000000000000000000000000
χ4966666666-1-1-1-10000000066-1-1-1-1-1-10000-1-1-1-100000000000000000000000000
χ5066666666-1-1-1-100000000-6-6-1-1-1-1-1-10000111100000000000000000000000000
χ51666666-6-6-1-1-1-1000000006-6-1-111110000-1-11100000000000000000000000000
χ52666666-6-6-1-1-1-100000000-66-1-11111000011-1-100000000000000000000000000
χ536666-6-66-6-1-1-1-1000000000011-1-1110000−i7i7−i7i700000000000000000000000000
χ546666-6-66-6-1-1-1-1000000000011-1-1110000i7−i7i7−i700000000000000000000000000
χ556666-6-6-66-1-1-1-100000000001111-1-10000−i7i7i7−i700000000000000000000000000
χ566666-6-6-66-1-1-1-100000000001111-1-10000i7−i7−i7i700000000000000000000000000
χ571212-12-120000-22-22000000000000−2i72i7000000000000000000000000000000000000
χ581212-12-120000-22-220000000000002i7−2i7000000000000000000000000000000000000
χ5912-1212-120000-222-200000000000000−2i72i70000000000000000000000000000000000
χ6012-1212-120000-222-2000000000000002i7−2i70000000000000000000000000000000000
χ6112-12-121212-1200-2-2220000000000-2200000000000000000000000000000000000000
χ6212-12-1212-121200-2-22200000000002-200000000000000000000000000000000000000

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