Finite Group Databasebeta

← Group #13167634

Character table — Group #13167634

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112488991616161818183636363636363636727211248899161616181818363636363636363672721124889916161618181836363636363636367272
order12423622661244424448888443612636666612121212612121224242424121236126366666121212126121212242424241212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ311111111111-1-111-1-1-111-1-11-111111111111-1-111-1-1-111-1-11-111111111111-1-111-1-1-111-1-11-1
χ411111111111-1-111-1-1-1-1-111-1111111111111-1-111-1-1-1-1-111-1111111111111-1-111-1-1-1-1-111-11
χ5111-11111-1-11111-11-1-11111-1-1111-11111-1-11111-11-1-11111-1-1111-11111-1-11111-11-1-11111-1-1
χ6111-11111-1-11111-11-1-1-1-1-1-111111-11111-1-11111-11-1-1-1-1-1-111111-11111-1-11111-11-1-1-1-1-1-111
χ7111-11111-1-11-1-11-1-11111-1-1-11111-11111-1-11-1-11-1-11111-1-1-11111-11111-1-11-1-11-1-11111-1-1-11
χ8111-11111-1-11-1-11-1-111-1-1111-1111-11111-1-11-1-11-1-111-1-1111-1111-11111-1-11-1-11-1-111-1-1111-1
χ9222222-2-222200-2-2000000000222222-2-222200-2-2000000000222222-2-222200-2-2000000000
χ10222-222-2-2-2-2200-22000000000222-222-2-2-2-2200-22000000000222-222-2-2-2-2200-22000000000
χ1122-20222200-222-20-20000000022-20222200-222-20-20000000022-20222200-222-20-200000000
χ1222-20222200-2-2-2-2020000000022-20222200-2-2-2-2020000000022-20222200-2-2-2-20200000000
χ1322-2022-2-200-2002002i−2i00000022-2022-2-200-2002002i−2i00000022-2022-2-200-2002002i−2i000000
χ1422-2022-2-200-200200−2i2i00000022-2022-2-200-200200−2i2i00000022-2022-2-200-200200−2i2i000000
χ152-2002-2-220002-2000002−22−2002-2002-2-220002-2000002−22−2002-2002-2-220002-2000002−22−200
χ162-2002-2-220002-200000−22−22002-2002-2-220002-200000−22−22002-2002-2-220002-200000−22−2200
χ172-2002-2-22000-22000002−2−22002-2002-2-22000-22000002−2−22002-2002-2-22000-22000002−2−2200
χ182-2002-2-22000-2200000−222−2002-2002-2-22000-2200000−222−2002-2002-2-22000-2200000−222−200
χ194-4004-44-400000000000000004-4004-44-400000000000000004-4004-44-40000000000000000
χ208888-1-100-1-1-100000000000008888-1-100-1-1-100000000000008888-1-100-1-1-10000000000000
χ21888-8-1-10011-10000000000000888-8-1-10011-10000000000000888-8-1-10011-10000000000000
χ2288-80-1-1003-31000000000000088-80-1-1003-31000000000000088-80-1-1003-310000000000000
χ2388-80-1-100-331000000000000088-80-1-100-331000000000000088-80-1-100-3310000000000000
χ2416-1600-2200000000000000000016-1600-2200000000000000000016-1600-22000000000000000000
χ25111111111111111111111111−1+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+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−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
χ26111111111111111111-1-1-1-1-1-1−1+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+i32−1+i321−i321−i321−i321−i321−i321−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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32
χ2711111111111-1-111-1-1-111-1-11-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32
χ2811111111111-1-111-1-1-1-1-111-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ29111-11111-1-11111-11-1-11111-1-1−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ30111-11111-1-11111-11-1-1-1-1-1-111−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ31111-11111-1-11-1-11-1-11111-1-1-11−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32
χ32111-11111-1-11-1-11-1-111-1-1111-1−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32
χ33222222-2-222200-2-2000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3001−i31−i3000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3001+i31+i3000000000
χ34222-222-2-2-2-2200-22000000000−1+i3−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i31−i3−1+i3001−i3−1+i3000000000−1−i3−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i31+i3−1−i3001+i3−1−i3000000000
χ3522-20222200-222-20-200000000−1+i3−1+i31−i30−1+i3−1+i3−1+i3−1+i3001−i3−1+i3−1+i31−i301−i300000000−1−i3−1−i31+i30−1−i3−1−i3−1−i3−1−i3001+i3−1−i3−1−i31+i301+i300000000
χ3622-20222200-2-2-2-20200000000−1+i3−1+i31−i30−1+i3−1+i3−1+i3−1+i3001−i31−i31−i31−i30−1+i300000000−1−i3−1−i31+i30−1−i3−1−i3−1−i3−1−i3001+i31+i31+i31+i30−1−i300000000
χ3722-2022-2-200-2002002i−2i000000−1+i3−1+i31−i30−1+i3−1+i31−i31−i3001−i300−1+i3002ζ14−2ζ14000000−1−i3−1−i31+i30−1−i3−1−i31+i31+i3001+i300−1−i3002ζ22−2ζ22000000
χ3822-2022-2-200-200200−2i2i000000−1+i3−1+i31−i30−1+i3−1+i31−i31−i3001−i300−1+i300−2ζ142ζ14000000−1−i3−1−i31+i30−1−i3−1−i31+i31+i3001+i300−1−i300−2ζ222ζ22000000
χ392-2002-2-220002-2000002−22−200−1+i31−i300−1+i31−i31−i3−1+i3000−1+i31−i300000ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ2300−1−i31+i300−1−i31+i31+i3−1−i3000−1−i31+i300000−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ1300
χ402-2002-2-220002-200000−22−2200−1+i31−i300−1+i31−i31−i3−1+i3000−1+i31−i300000−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ2300−1−i31+i300−1−i31+i31+i3−1−i3000−1−i31+i300000ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ1300
χ412-2002-2-22000-22000002−2−2200−1+i31−i300−1+i31−i31−i3−1+i30001−i3−1+i300000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ2300−1−i31+i300−1−i31+i31+i3−1−i30001+i3−1−i300000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ1300
χ422-2002-2-22000-2200000−222−200−1+i31−i300−1+i31−i31−i3−1+i30001−i3−1+i300000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ2300−1−i31+i300−1−i31+i31+i3−1−i30001+i3−1−i300000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ1300
χ434-4004-44-40000000000000000−2+2i32−2i300−2+2i32−2i3−2+2i32−2i30000000000000000−2−2i32+2i300−2−2i32+2i3−2−2i32+2i30000000000000000
χ448888-1-100-1-1-10000000000000−4+4i3−4+4i3−4+4i3−4+4i31−i321−i32001−i321−i321−i320000000000000−4−4i3−4−4i3−4−4i3−4−4i31+i321+i32001+i321+i321+i320000000000000
χ45888-8-1-10011-10000000000000−4+4i3−4+4i3−4+4i34−4i31−i321−i3200−1+i32−1+i321−i320000000000000−4−4i3−4−4i3−4−4i34+4i31+i321+i3200−1−i32−1−i321+i320000000000000
χ4688-80-1-1003-310000000000000−4+4i3−4+4i34−4i301−i321−i3200−3+3i323−3i32−1+i320000000000000−4−4i3−4−4i34+4i301+i321+i3200−3−3i323+3i32−1−i320000000000000
χ4788-80-1-100-3310000000000000−4+4i3−4+4i34−4i301−i321−i32003−3i32−3+3i32−1+i320000000000000−4−4i3−4−4i34+4i301+i321+i32003+3i32−3−3i32−1−i320000000000000
χ4816-1600-22000000000000000000−8+8i38−8i3001−i3−1+i3000000000000000000−8−8i38+8i3001+i3−1−i3000000000000000000
χ49111111111111111111111111−1−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−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+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
χ50111111111111111111-1-1-1-1-1-1−1−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−i32−1−i321+i321+i321+i321+i321+i321+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+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32
χ5111111111111-1-111-1-1-111-1-11-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32
χ5211111111111-1-111-1-1-1-1-111-11−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ53111-11111-1-11111-11-1-11111-1-1−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ54111-11111-1-11111-11-1-1-1-1-1-111−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ55111-11111-1-11-1-11-1-11111-1-1-11−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32
χ56111-11111-1-11-1-11-1-111-1-1111-1−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32
χ57222222-2-222200-2-2000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3001+i31+i3000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3001−i31−i3000000000
χ58222-222-2-2-2-2200-22000000000−1−i3−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i31+i3−1−i3001+i3−1−i3000000000−1+i3−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i31−i3−1+i3001−i3−1+i3000000000
χ5922-20222200-222-20-200000000−1−i3−1−i31+i30−1−i3−1−i3−1−i3−1−i3001+i3−1−i3−1−i31+i301+i300000000−1+i3−1+i31−i30−1+i3−1+i3−1+i3−1+i3001−i3−1+i3−1+i31−i301−i300000000
χ6022-20222200-2-2-2-20200000000−1−i3−1−i31+i30−1−i3−1−i3−1−i3−1−i3001+i31+i31+i31+i30−1−i300000000−1+i3−1+i31−i30−1+i3−1+i3−1+i3−1+i3001−i31−i31−i31−i30−1+i300000000
χ6122-2022-2-200-2002002i−2i000000−1−i3−1−i31+i30−1−i3−1−i31+i31+i3001+i300−1−i3002ζ22−2ζ22000000−1+i3−1+i31−i30−1+i3−1+i31−i31−i3001−i300−1+i3002ζ14−2ζ14000000
χ6222-2022-2-200-200200−2i2i000000−1−i3−1−i31+i30−1−i3−1−i31+i31+i3001+i300−1−i300−2ζ222ζ22000000−1+i3−1+i31−i30−1+i3−1+i31−i31−i3001−i300−1+i300−2ζ142ζ14000000
χ632-2002-2-220002-2000002−22−200−1−i31+i300−1−i31+i31+i3−1−i3000−1−i31+i300000−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ1300−1+i31−i300−1+i31−i31−i3−1+i3000−1+i31−i300000ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ2300
χ642-2002-2-220002-200000−22−2200−1−i31+i300−1−i31+i31+i3−1−i3000−1−i31+i300000ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ1300−1+i31−i300−1+i31−i31−i3−1+i3000−1+i31−i300000−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ2300
χ652-2002-2-22000-22000002−2−2200−1−i31+i300−1−i31+i31+i3−1−i30001+i3−1−i300000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ1300−1+i31−i300−1+i31−i31−i3−1+i30001−i3−1+i300000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ2300
χ662-2002-2-22000-2200000−222−200−1−i31+i300−1−i31+i31+i3−1−i30001+i3−1−i300000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ1300−1+i31−i300−1+i31−i31−i3−1+i30001−i3−1+i300000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ2300
χ674-4004-44-40000000000000000−2−2i32+2i300−2−2i32+2i3−2−2i32+2i30000000000000000−2+2i32−2i300−2+2i32−2i3−2+2i32−2i30000000000000000
χ688888-1-100-1-1-10000000000000−4−4i3−4−4i3−4−4i3−4−4i31+i321+i32001+i321+i321+i320000000000000−4+4i3−4+4i3−4+4i3−4+4i31−i321−i32001−i321−i321−i320000000000000
χ69888-8-1-10011-10000000000000−4−4i3−4−4i3−4−4i34+4i31+i321+i3200−1−i32−1−i321+i320000000000000−4+4i3−4+4i3−4+4i34−4i31−i321−i3200−1+i32−1+i321−i320000000000000
χ7088-80-1-1003-310000000000000−4−4i3−4−4i34+4i301+i321+i3200−3−3i323+3i32−1−i320000000000000−4+4i3−4+4i34−4i301−i321−i3200−3+3i323−3i32−1+i320000000000000
χ7188-80-1-100-3310000000000000−4−4i3−4−4i34+4i301+i321+i32003+3i32−3−3i32−1−i320000000000000−4+4i3−4+4i34−4i301−i321−i32003−3i32−3+3i32−1+i320000000000000
χ7216-1600-22000000000000000000−8−8i38+8i3001+i3−1−i3000000000000000000−8+8i38−8i3001−i3−1+i3000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.