Finite Group Databasebeta

← Group #13051949

Character table — Group #13051949

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122446666777777778812121212121214141414242424242828282828282828282828282828282856565656565656565656
order12224424714141433666666441414282828281212121228282828668888121224242424242424242466121212121212
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111-1-11111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i321111−1−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−i32−1+i32-1-1-1-1−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−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+i32-1-1-1-1−1−i32−1+i321111−1−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−i32−1+i32-1-1-1-1−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+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−i321111−1+i32−1−i321111−1+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+i32−1−i32-1-1-1-1−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+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−i32-1-1-1-1−1+i32−1−i321111−1+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+i32−1−i32-1-1-1-1−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32
χ13111111-1-11111111111111-1-1-111-1-11111-1-111-1-111-1-1-1-111-1-111-1-11-1111-11-1-1-1
χ14111111-1-11111111111111-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-111-1-111-11-1-11-11-111
χ15111111-1-1111111111111-11-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111-1-1-11-1-1-11-1111
χ16111111-1-1111111111111-11-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1111-111-11-11-1-1
χ17111111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-1-111-1-1−1−i32−1+i32−1−i32−1+i32-1-1111+i321−i3211-1-11+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32
χ18111111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-1-111-1-1−1−i32−1+i32−1−i32−1+i32-1-1111+i321−i32-1-1111+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32
χ19111111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-1-111-1-1−1−i32−1+i32−1−i32−1+i3211-1-11+i321−i3211-1-11+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-111+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i32
χ20111111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-1-111-1-1−1−i32−1+i32−1−i32−1+i3211-1-11+i321−i32-1-1111+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i32
χ21111111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-1-111-1-1−1+i32−1−i32−1+i32−1−i32-1-1111−i321+i3211-1-11−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32
χ22111111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-1-111-1-1−1+i32−1−i32−1+i32−1−i32-1-1111−i321+i32-1-1111−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32
χ23111111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-1-111-1-1−1+i32−1−i32−1+i32−1−i3211-1-11−i321+i3211-1-11−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-111−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i32
χ24111111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-1-111-1-1−1+i32−1−i32−1+i32−1−i3211-1-11−i321+i32-1-1111−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i32
χ252222-2-22-22222222222220022-2-2-2-2-2-2-2-20000220000-2-2000000000000000000
χ262222-2-22-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i30022-2-2-2-21+i31−i31+i31−i30000−1−i3−1+i300001+i31−i3000000000000000000
χ272222-2-22-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i30022-2-2-2-21−i31+i31−i31+i30000−1+i3−1−i300001−i31+i3000000000000000000
χ282222-2-2-2222222222222200-2-2-2-222-2-2-2-20000-2-2000022000000000000000000
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−i300001+i31−i30000−1−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+i300001−i31+i30000−1+i3−1−i3000000000000000000
χ312-22-22-2002-2-2222-2-22-22-200002-20022-2-2000000002i−2i00002i−2i002i−2i0000000000
χ322-22-22-2002-2-2222-2-22-22-200002-20022-2-200000000−2i2i0000−2i2i00−2i2i0000000000
χ332-22-22-2002-2-22−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i300002-200−1−i3−1+i31+i31−i3000000002i−2i00002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ790000000000
χ342-22-22-2002-2-22−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i300002-200−1−i3−1+i31+i31−i300000000−2i2i0000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ790000000000
χ352-22-22-2002-2-22−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i300002-200−1+i3−1−i31−i31+i3000000002i−2i00002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ830000000000
χ362-22-22-2002-2-22−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i300002-200−1+i3−1−i31−i31+i300000000−2i2i0000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ830000000000
χ372-22-2-22002-2-2222-2-22-22-20000-2200-2-2220000002-200002-2002-2000000000000
χ382-22-2-22002-2-2222-2-22-22-20000-2200-2-222000000-220000-2200-22000000000000
χ392-22-2-22002-2-22−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000-22001+i31−i3−1−i3−1+i30000002-20000−1−i31+i300−1+i31−i3000000000000
χ402-22-2-22002-2-22−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000-22001+i31−i3−1−i3−1+i3000000-2200001+i3−1−i3001−i3−1+i3000000000000
χ412-22-2-22002-2-22−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000-22001−i31+i3−1+i3−1−i30000002-20000−1+i31−i300−1−i31+i3000000000000
χ422-22-2-22002-2-22−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000-22001−i31+i3−1+i3−1−i3000000-2200001−i3−1+i3001+i3−1−i3000000000000
χ4344-4-4000044-4-44444-4-4-4-4000000000000000000000000000000000000000000
χ4444-4-4000044-4-4−2−2i3−2+2i3−2−2i3−2+2i32+2i32+2i32−2i32−2i3000000000000000000000000000000000000000000
χ4544-4-4000044-4-4−2+2i3−2−2i3−2+2i3−2−2i32−2i32−2i32+2i32+2i3000000000000000000000000000000000000000000
χ464-4-4400004-44-444-4-4-44-44000000000000000000000000000000000000000000
χ474-4-4400004-44-4−2−2i3−2+2i32+2i32−2i32+2i3−2−2i32−2i3−2+2i3000000000000000000000000000000000000000000
χ484-4-4400004-44-4−2+2i3−2−2i32−2i32+2i32−2i3−2+2i32+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
χ51666666-6-6-1-1-1-1000000006-611-1-111000011-1-100000000000000000000000000
χ52666666-6-6-1-1-1-100000000-6611-1-1110000-1-11100000000000000000000000000
χ536666-6-66-6-1-1-1-10000000000-1-111110000−i7i7−i7i700000000000000000000000000
χ546666-6-66-6-1-1-1-10000000000-1-111110000i7−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
χ571212-12-120000-2-2220000000000−2i72i700000000000000000000000000000000000000
χ581212-12-120000-2-22200000000002i7−2i700000000000000000000000000000000000000
χ5912-1212-1212-1200-222-2000000000000-22000000000000000000000000000000000000
χ6012-1212-12-121200-222-20000000000002-2000000000000000000000000000000000000
χ6112-12-12120000-22-220000000000000027−270000000000000000000000000000000000
χ6212-12-12120000-22-2200000000000000−27270000000000000000000000000000000000

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