Finite Group Databasebeta

← Group #14316804

Character table — Group #14316804

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222222222444444444444488888888888888888888888888888881616161616161616161640404040404040404040404048484848484848484848120120240
order1223556661010224101015153030303030304466101010101212121212202020202020606060606060606060606060202030303030606060602244666612121212442020202020202020248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ5111111111111111111111111-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-11-111-1-111-1-11-11111-1-1-1-111-1
χ6111111111111111111111111-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-11-111-1-111-1-1-11-1-1-1-11111-1-11
χ7111111111111111111111111-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11-11-1-111-1-1111-11111-1-1-1-1-1-11
χ8111111111111111111111111-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11-11-1-111-1-111-11-1-1-1-1111111-1
χ9222222222222-2-22222222222002-222-2-2-20000-2-2000000000000-2-2-2-20022-2-20000020-2002200-2-20000000000000
χ10222222222222-2-22222222222002-222-2-2-20000-2-2000000000000-2-2-2-20022-2-200000-20200-2-200220000000000000
χ1122222222222-22-2222222222200-22-2-222-20000-2-2000000000000-2-2-2-200-2-222000020-202200-2-2000000000000000
χ1222222222222-22-2222222222200-22-2-222-20000-2-2000000000000-2-2-2-200-2-2220000-2020-2-20022000000000000000
χ1322222222222-2-2222222222222-2-2-2-2-2-2-2222-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222220000000000000000000000000
χ1422222222222-2-222222222222-22-2-2-2-2-2-22-2-222222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000
χ152222−1−52−1+52222−1−52−1+52222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+52−1−52−1+5222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5200000000000022−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000
χ162222−1−52−1+52222−1−52−1+52222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+52−1−52−1+5222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52000000000000-2-21+521+521−521−521+521+521−521−52000
χ172222−1−52−1+52222−1−52−1+52222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+522-2-2-2-2−1−52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+52−1−52−1+521+521+521−521−520000000000002-2−1−52−1−52−1+52−1+521+521+521−521−52000
χ182222−1−52−1+52222−1−52−1+52222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+522-2-2-2-2−1−52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+52−1−52−1+521+521+521−521−52000000000000-221+521+521−521−52−1−52−1−52−1+52−1+52000
χ192222−1−52−1+52222−1−52−1+52-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2-2-21+521−521+521−52222-2-2−1−52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+5200000000000000−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47000
χ202222−1−52−1+52222−1−52−1+52-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2-2-21+521−521+521−52222-2-2−1−52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+5200000000000000ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47000
χ212222−1−52−1+52222−1−52−1+52-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-22-2-21+521−521+521−522-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−521+521−521+521+521−521−5200000000000000−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47000
χ222222−1−52−1+52222−1−52−1+52-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-22-2-21+521−521+521−522-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−521+521−521+521+521−521−5200000000000000ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47000
χ232222−1+52−1−52222−1+52−1−52222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1−52−1+52−1−5222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5200000000000022−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000
χ242222−1+52−1−52222−1+52−1−52222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1−52−1+52−1−5222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52000000000000-2-21−521−521+521+521−521−521+521+52000
χ252222−1+52−1−52222−1+52−1−52222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−522-2-2-2-2−1+52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−52−1+52−1−521−521−521+521+520000000000002-2−1+52−1+52−1−52−1−521−521−521+521+52000
χ262222−1+52−1−52222−1+52−1−52222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−522-2-2-2-2−1+52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−52−1+52−1−521−521−521+521+52000000000000-221−521−521+521+52−1+52−1+52−1−52−1−52000
χ272222−1+52−1−52222−1+52−1−52-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2-2-21−521+521−521+52222-2-2−1+52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−5200000000000000ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59000
χ282222−1+52−1−52222−1+52−1−52-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2-2-21−521+521−521+52222-2-2−1+52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−5200000000000000−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59000
χ292222−1+52−1−52222−1+52−1−52-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-22-2-21−521+521−521+522-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+521−521+521−521−521+521+5200000000000000ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59000
χ302222−1+52−1−52222−1+52−1−52-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-22-2-21−521+521−521+522-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+521−521+521−521−521+521+5200000000000000−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59000
χ31222-122-1-1-12222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000
χ32222-122-1-1-12222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000
χ33222-122-1-1-12222222-1-1-1-1-1-1-1-1-2-2-1-12222-1111122-2-2-2-211111111-1-1-1-1-2-2-1-1-1-111112-22-2-1-111-1-1110000000000000
χ34222-122-1-1-12222222-1-1-1-1-1-1-1-1-2-2-1-12222-1111122-2-2-2-211111111-1-1-1-1-2-2-1-1-1-11111-22-2211-1-111-1-10000000000000
χ35222-122-1-1-1222-2-222-1-1-1-1-1-1-1-100-1122-2-21−i3i3−i3i3-2-20000−i3−i3i3i3−i3−i3i3i3111100-1-111−i3i3−i3i3020-2−i3i3-1-1−i3i3110000000000000
χ36222-122-1-1-1222-2-222-1-1-1-1-1-1-1-100-1122-2-21−i3i3−i3i3-2-20000−i3−i3i3i3−i3−i3i3i3111100-1-111−i3i3−i3i30-202i3−i311i3−i3-1-10000000000000
χ37222-122-1-1-1222-2-222-1-1-1-1-1-1-1-100-1122-2-21i3−i3i3−i3-2-20000i3i3−i3−i3i3i3−i3−i3111100-1-111i3−i3i3−i3020-2i3−i3-1-1i3−i3110000000000000
χ38222-122-1-1-1222-2-222-1-1-1-1-1-1-1-100-1122-2-21i3−i3i3−i3-2-20000i3i3−i3−i3i3i3−i3−i3111100-1-111i3−i3i3−i30-202−i3i311−i3i3-1-10000000000000
χ39222-122-1-1-122-22-222-1-1-1-1-1-1-1-1001-1-2-2221−i3i3i3−i3-2-20000i3i3−i3−i3i3i3−i3−i311110011-1-1−i3i3−i3i320-20-1-1−i3i311−i3i30000000000000
χ40222-122-1-1-122-22-222-1-1-1-1-1-1-1-1001-1-2-2221−i3i3i3−i3-2-20000i3i3−i3−i3i3i3−i3−i311110011-1-1−i3i3−i3i3-202011i3−i3-1-1i3−i30000000000000
χ41222-122-1-1-122-22-222-1-1-1-1-1-1-1-1001-1-2-2221i3−i3−i3i3-2-20000−i3−i3i3i3−i3−i3i3i311110011-1-1i3−i3i3−i320-20-1-1i3−i311i3−i30000000000000
χ42222-122-1-1-122-22-222-1-1-1-1-1-1-1-1001-1-2-2221i3−i3−i3i3-2-20000−i3−i3i3i3−i3−i3i3i311110011-1-1i3−i3i3−i3-202011−i3i3-1-1−i3i30000000000000
χ43222-122-1-1-122-2-2222-1-1-1-1-1-1-1-12-211-2-2-2-2-1-1-11122-2-2-2-211111111-1-1-1-1221111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000
χ44222-122-1-1-122-2-2222-1-1-1-1-1-1-1-12-211-2-2-2-2-1-1-11122-2-2-2-211111111-1-1-1-1221111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000
χ45222-122-1-1-122-2-2222-1-1-1-1-1-1-1-1-2211-2-2-2-2-111-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111110000−i3i3i3−i3i3−i3−i3i30000000000000
χ46222-122-1-1-122-2-2222-1-1-1-1-1-1-1-1-2211-2-2-2-2-111-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111110000i3−i3−i3i3−i3i3i3−i30000000000000
χ474444−1−5−1+5444−1−5−1+54-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5004-4−1−5−1+51+51−5-400001+51−50000000000001+51+51−51−500−1−5−1+51+51−500000000000000000000000000000
χ484444−1−5−1+5444−1−5−1+5-44-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+500-441+51−5−1−5−1+5-400001+51−50000000000001+51+51−51−5001+51−5−1−5−1+500000000000000000000000000000
χ494444−1+5−1−5444−1+5−1−54-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5004-4−1+5−1−51−51+5-400001−51+50000000000001−51−51+51+500−1+5−1−51−51+500000000000000000000000000000
χ504444−1+5−1−5444−1+5−1−5-44-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−500-441−51+5−1+5−1−5-400001−51+50000000000001−51−51+51+5001−51+5−1+5−1−500000000000000000000000000000
χ51444-2−1−5−1+5-2-2-2−1−5−1+5444−1−5−1+51+521−521+521+521−521−521+521−5244-2-2−1−5−1+5−1−5−1+5-2-2-2-2-2−1−5−1+5−1−5−1−5−1+5−1+51+521+521+521+521−521−521−521−521+521+521−521−52−1−5−1+51+521−521+521−521+521+521−521−520000000000000000000000000
χ52444-2−1−5−1+5-2-2-2−1−5−1+5444−1−5−1+51+521−521+521+521−521−521+521−52-4-4-2-2−1−5−1+5−1−5−1+5-22222−1−5−1+51+51+51−51−5−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521−521−521+51−51+521−521+521−52−1−52−1−52−1+52−1+520000000000000000000000000
χ53444-2−1−5−1+5-2-2-2−1−5−1+54-4-4−1−5−1+51+521−521+521+521−521−521+521−5200-22−1−5−1+51+51−52−2i32i3−2i32i31+51−50000ζ14+ζ26−ζ34−ζ46ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46−ζ14−ζ26+ζ34+ζ46ζ2−ζ22+ζ38−ζ58ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58−ζ2+ζ22−ζ38+ζ58−1−52−1−52−1+52−1+52001+521−52−1−52−1+52ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ580000000000000000000000000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.