Finite Group Databasebeta

← Group #72343933

Character table — Group #72343933

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91
size1111224444666688812121212121212121212161616161616161616161616162424242424242424242424242424323232323232323232484848486464646464646464646464646464646464649696128128128128
order12224422882244222222222444422334666666882222244448888846666121212124444666666661212242424242424242448661212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111111−1−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+i32−1−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
χ311111111111111111111111111111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111111−1+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−i32−1+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
χ4111111111111111-1-11111111111-1-111-1111111-1-111111111111111-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-111-1-1
χ5111111111111111-1-11111111111-1-1−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111111111111111-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1−1−i32−1+i321+i321−i32
χ6111111111111111-1-11111111111-1-1−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111111111111111-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1−1+i32−1−i321−i321+i32
χ711111111-1-11111-111111111111111111111111-1-111-1-1-111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ811111111-1-11111-111111111111111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-1-111-1-1-1-1-1-1-1-1−1−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+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321−i321+i321−i32
χ911111111-1-11111-111111111111111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-1-111-1-1-1-1-1-1-1-1−1+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−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321+i321−i321+i32
χ1011111111-1-11111-1-1-11111111111-1-111-11111111111-1-1-111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-111-1-11111-1-111
χ1111111111-1-11111-1-1-11111111111-1-1−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-111-1-1-1-1-1-1-111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32111+i321−i32−1−i32−1+i32
χ1211111111-1-11111-1-1-11111111111-1-1−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-111-1-1-1-1-1-1-111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32111−i321+i32−1+i32−1−i32
χ13111111-1-1111111-1111111-1-11111-1-111111111111-1-1-1-1-1-1-1-1-111111-11111111111-1-1-1-1-1-1-1-1-1-11111111111-11-1-1-1-1
χ14111111-1-1111111-1111111-1-11111-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-1-1-1-1-1-111111-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-11+i321+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+i32-111+i321−i321+i321−i32
χ15111111-1-1111111-1111111-1-11111-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-1-1-1-1-1-111111-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-11−i321−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−i32-111−i321+i321−i321+i32
χ16111111-1-1111111-1-1-11111-1-111111111-1111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-111-1-111-1-111-1-11-1-1-111
χ17111111-1-1111111-1-1-11111-1-1111111−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-11111111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-11+i321−i32−1−i32−1+i32
χ18111111-1-1111111-1-1-11111-1-1111111−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-11111111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-11−i321+i32−1+i32−1−i32
χ19111111-1-1-1-111111111111-1-11111-1-1111111111-1-1-1-1111-1-111-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11111
χ20111111-1-1-1-111111111111-1-11111-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1111-1-111-1-1-1-1-11−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321-1−1−i32−1+i32−1−i32−1+i32
χ21111111-1-1-1-111111111111-1-11111-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1111-1-111-1-1-1-1-11−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321-1−1+i32−1−i32−1+i32−1−i32
χ22111111-1-1-1-111111-1-11111-1-111111111-111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-111-1111-1-1
χ23111111-1-1-1-111111-1-11111-1-1111111−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1111-1-111-1-1-1-1-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-11−1−i32−1+i321+i321−i32
χ24111111-1-1-1-111111-1-11111-1-1111111−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1111-1-111-1-1-1-1-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-11−1+i32−1−i321−i321+i32
χ252222-2-2000022-2-202222-2-20022-2-20022-2222222000000000000000002222-2-2-2-22-20000000000-2-200000000000000
χ262222-2-2000022-2-202222-2-20022-2-200−1−i3−1+i3-2−1−i3−1+i3−1−i3−1−i3−1+i3−1+i300000000000000000−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i32-200000000001+i31−i300000000000000
χ272222-2-2000022-2-202222-2-20022-2-200−1+i3−1−i3-2−1+i3−1−i3−1+i3−1+i3−1−i3−1−i300000000000000000−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i32-200000000001−i31+i300000000000000
χ282222-2-2000022-2-20-2-222-2-20022-2-20022222222200000000000000000-2-2-2-2-2-2-2-2-2200000000002200000000000000
χ292222-2-2000022-2-20-2-222-2-20022-2-200−1−i3−1+i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3000000000000000001+i31+i31−i31−i31+i31+i31−i31−i3-220000000000−1−i3−1+i300000000000000
χ302222-2-2000022-2-20-2-222-2-20022-2-200−1+i3−1−i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3000000000000000001−i31−i31+i31+i31−i31−i31+i31+i3-220000000000−1+i3−1−i300000000000000
χ312-2-222-20000-22-220002-22-2002-22-22-2220-2-22-22-20000000000000000000002-22-2002-2002-2002-20000000000000000
χ322-2-222-20000-22-220002-22-2002-22-22-2−1−i3−1+i301+i31−i3−1−i31+i3−1+i31−i3000000000000000000000−1−i31+i3−1+i31−i3002-200−1−i31+i300−1+i31−i30000000000000000
χ332-2-222-20000-22-220002-22-2002-22-22-2−1+i3−1−i301−i31+i3−1+i31−i3−1−i31+i3000000000000000000000−1+i31−i3−1−i31+i3002-200−1+i31−i300−1−i31+i30000000000000000
χ342-2-222-20000-22-220002-22-2002-22-2-22220-2-22-22-20000000000000000000002-22-200-2200-2200-220000000000000000
χ352-2-222-20000-22-220002-22-2002-22-2-22−1−i3−1+i301+i31−i3−1−i31+i3−1+i31−i3000000000000000000000−1−i31+i3−1+i31−i300-22001+i3−1−i3001−i3−1+i30000000000000000
χ362-2-222-20000-22-220002-22-2002-22-2-22−1+i3−1−i301−i31+i3−1+i31−i3−1−i31+i3000000000000000000000−1+i31−i3−1−i31+i300-22001−i3−1+i3001+i3−1−i30000000000000000
χ372-2-22-222-200-222-20002-2-222-22-2-2200220-2-22-22-2002-20002-2000000000000-22-2200002-2002-2000000000000000000
χ382-2-22-222-200-222-20002-2-222-22-2-2200−1−i3−1+i301+i31−i3−1−i31+i3−1+i31−i3002-20002-20000000000001+i3−1−i31−i3−1+i30000−1−i31+i300−1+i31−i3000000000000000000
χ392-2-22-222-200-222-20002-2-222-22-2-2200−1+i3−1−i301−i31+i3−1+i31−i3−1−i31+i3002-20002-20000000000001−i3−1+i31+i3−1−i30000−1+i31−i300−1−i31+i3000000000000000000
χ402-2-22-22-2200-222-20002-2-22-222-2-2200220-2-22-22-200-22000-22000000000000-22-220000-2200-22000000000000000000
χ412-2-22-22-2200-222-20002-2-22-222-2-2200−1−i3−1+i301+i31−i3−1−i31+i3−1+i31−i300-22000-220000000000001+i3−1−i31−i3−1+i300001+i3−1−i3001−i3−1+i3000000000000000000
χ422-2-22-22-2200-222-20002-2-22-222-2-2200−1+i3−1−i301−i31+i3−1+i31−i3−1−i31+i300-22000-220000000000001−i3−1+i31+i3−1−i300001−i3−1+i3001+i3−1−i3000000000000000000
χ4333333333333333333-1-1-1-133-1-1-1-13300300000033-1-13-1-1-1-1-1-13-1-1-1-1300000000-1-1-1-1000000000000000000-1-10000
χ44333333333333333-3-3-1-1-1-133-1-1-1-1-3-300-3000000-3-3-1-13-1-1-1-1-1-13-1-1-1-1-3000000001111000000000000000000110000
χ4533333333-3-33333-333-1-1-1-133-1-1-1-133003000000-3-3-1-1-311-1-111-31111-300000000-1-1-1-1000000000000000000110000
χ4633333333-3-33333-3-3-3-1-1-1-133-1-1-1-1-3-300-300000033-1-1-311-1-111-311113000000001111000000000000000000-1-10000
χ47333333-3-3333333-333-1-1-1-1-3-3-1-1-1-1-3-30030000003311-31111113-1-1-1-1-300000000-1-1110000000000000000001-10000
χ48333333-3-3333333-3-3-3-1-1-1-1-3-3-1-1-1-13300-3000000-3-311-31111113-1-1-1-130000000011-1-1000000000000000000-110000
χ49333333-3-3-3-33333333-1-1-1-1-3-3-1-1-1-1-3-3003000000-3-3113-1-111-1-1-31111300000000-1-111000000000000000000-110000
χ50333333-3-3-3-333333-3-3-1-1-1-1-3-3-1-1-1-13300-300000033113-1-111-1-1-31111-30000000011-1-10000000000000000001-10000
χ516666666666-2-2-2-260022-2-2-2-2-2-222000000000000022-222-2-2-2-2-222-2-20000000000000000000000000000000000000
χ526666666666-2-2-2-2600-2-222-2-222-2-20000000000000-2-2-2-2-22222-2-2-2220000000000000000000000000000000000000
χ5366666666-6-6-2-2-2-2-60022-2-2-2-2-2-2220000000000000222-2-2-2-2222-2-2220000000000000000000000000000000000000
χ5466666666-6-6-2-2-2-2-600-2-222-2-222-2-20000000000000-2-222222-2-2222-2-20000000000000000000000000000000000000
χ55666666-6-666-2-2-2-2-60022-2-222-2-2220000000000000-2-22-2-22222-222-2-20000000000000000000000000000000000000
χ56666666-6-666-2-2-2-2-600-2-2222222-2-2000000000000022222-2-2-2-2-2-2-2220000000000000000000000000000000000000
χ57666666-6-6-6-6-2-2-2-260022-2-222-2-2220000000000000-2-2-22222-2-22-2-2220000000000000000000000000000000000000
χ58666666-6-6-6-6-2-2-2-2600-2-2222222-2-2000000000000022-2-2-2-2-222222-2-20000000000000000000000000000000000000
χ596666-6-6000066-6-6066-2-22200-2-2220000-60000000000000000000000000000000-2200000000000000000000000000
χ606666-6-6000066-6-60-6-6-2-22200-2-2220000600000000000000000000000000000002-200000000000000000000000000
χ616-6-666-60000-66-66000-22-2200-22-226-6000000000000000000000000000000000000-22000000000000000000000000
χ626-6-666-60000-66-66000-22-2200-22-22-660000000000000000000000000000000000002-2000000000000000000000000
χ636-6-66-666-6002-2-220002-22-2-22-22-2200000000000002-204-4-220004-4000000000000000000000000000000000000000
χ646-6-66-666-6002-2-220002-22-2-22-22-2200000000000002-20-44-22000-44000000000000000000000000000000000000000
χ656-6-66-666-6002-2-22000-22-22-222-22-20000000000000-220002-24-40004-40000000000000000000000000000000000000
χ666-6-66-666-6002-2-22000-22-22-222-22-20000000000000-220002-2-44000-440000000000000000000000000000000000000
χ676-6-66-666-600-666-6000-222-26-6-222-20000000000000-22000-2200000000000000000000000000000000000000000000
χ686-6-66-66-66002-2-220002-22-22-2-22-220000000000000-2204-42-2000-44000000000000000000000000000000000000000
χ696-6-66-66-66002-2-220002-22-22-2-22-220000000000000-220-442-20004-4000000000000000000000000000000000000000
χ706-6-66-66-66002-2-22000-22-222-22-22-200000000000002-2000-224-4000-440000000000000000000000000000000000000
χ716-6-66-66-66002-2-22000-22-222-22-22-200000000000002-2000-22-440004-40000000000000000000000000000000000000
χ726-6-66-66-6600-666-6000-222-2-66-222-200000000000002-20002-200000000000000000000000000000000000000000000
χ738-88-8000042−42000004-4000000000000220-2-2-22-2222−220000000000000002-22-20000000000000000002−22−22−22−2000000
χ748-88-8000042−42000004-4000000000000−1−i3−1+i301+i31−i31+i3−1−i31−i3−1+i322−22000000000000000−1−i31+i3−1+i31−i3000000000000000000−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23000000
χ758-88-8000042−42000004-4000000000000−1+i3−1−i301−i31+i31−i3−1+i31+i3−1−i322−22000000000000000−1+i31−i3−1−i31+i3000000000000000000ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13000000
χ768-88-8000042−4200000-44000000000000220-2-2-22-22−2222000000000000000-22-220000000000000000002−2−222−2−22000000
χ778-88-8000042−4200000-44000000000000−1−i3−1+i301+i31−i31+i3−1−i31−i3−1+i3−22220000000000000001+i3−1−i31−i3−1+i3000000000000000000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23000000
χ788-88-8000042−4200000-44000000000000−1+i3−1−i301−i31+i31−i3−1+i31+i3−1−i3−22220000000000000001−i3−1+i31+i3−1−i3000000000000000000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13000000
χ798-88-80000−4242000004-4000000000000220-2-2-22-22−22220000000000000002-22-2000000000000000000−22−22−22−22000000
χ808-88-80000−4242000004-4000000000000−1−i3−1+i301+i31−i31+i3−1−i31−i3−1+i3−2222000000000000000−1−i31+i3−1+i31−i3000000000000000000ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23000000
χ818-88-80000−4242000004-4000000000000−1+i3−1−i301−i31+i31−i3−1+i31+i3−1−i3−2222000000000000000−1+i31−i3−1−i31+i3000000000000000000−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13000000
χ828-88-80000−424200000-44000000000000220-2-2-22-2222−22000000000000000-22-22000000000000000000−222−2−222−2000000
χ838-88-80000−424200000-44000000000000−1−i3−1+i301+i31−i31+i3−1−i31−i3−1+i322−220000000000000001+i3−1−i31−i3−1+i3000000000000000000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23000000
χ848-88-80000−424200000-44000000000000−1+i3−1−i301−i31+i31−i3−1+i31+i3−1−i322−220000000000000001−i3−1+i31+i3−1−i3000000000000000000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13000000
χ8512121212-12-120000-4-444000444400-4-4-4-40000000000000000000000000000000000000000000000000000000000000000
χ8612121212-12-120000-4-444000-4-4-4-40044440000000000000000000000000000000000000000000000000000000000000000
χ8712-12-121212-1200004-44-40004-4-4400-444-40000000000000000000000000000000000000000000000000000000000000000
χ8812-12-121212-1200004-44-4000-444-4004-4-440000000000000000000000000000000000000000000000000000000000000000
χ891616-16-16000000000000000000000000044044-4-4-4-400000000000000000000000000000000000000000000000000000
χ901616-16-160000000000000000000000000−2−2i3−2+2i30−2−2i3−2+2i32+2i32+2i32−2i32−2i300000000000000000000000000000000000000000000000000000
χ911616-16-160000000000000000000000000−2+2i3−2−2i30−2+2i3−2−2i32−2i32−2i32+2i32+2i300000000000000000000000000000000000000000000000000000

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