Finite Group Databasebeta

← Group #88773

Character table — Group #88773

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size112222244444412121212121218181122222444444121212121212181811222224444441212121212121818
order12334663612121212246612128836331266361212121261266121224243633126636121212126126612122424
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-111-1-1-1-111111111111111-111-1-1-1-111111111111111-111-1-1-1-1
χ31111111111111-11-1-111-1-11111111111111-11-1-111-1-11111111111111-11-1-111-1-1
χ41111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-111
χ52222-22222-2-2-2-2000000002222-22222-2-2-2-2000000002222-22222-2-2-2-200000000
χ6222-12-12-1-1-12-1-120-1-10000222-12-12-1-1-12-1-120-1-10000222-12-12-1-1-12-1-120-1-10000
χ7222-12-12-1-1-12-1-1-20110000222-12-12-1-1-12-1-1-20110000222-12-12-1-1-12-1-1-20110000
χ8222-1-2-12-1-11-21100−i3i30000222-1-2-12-1-11-21100−i3i30000222-1-2-12-1-11-21100−i3i30000
χ9222-1-2-12-1-11-21100i3−i30000222-1-2-12-1-11-21100i3−i30000222-1-2-12-1-11-21100i3−i30000
χ1022-1222-1-1-12-1-1-10200-1-10022-1222-1-1-12-1-1-10200-1-10022-1222-1-1-12-1-1-10200-1-100
χ1122-1222-1-1-12-1-1-10-200110022-1222-1-1-12-1-1-10-200110022-1222-1-1-12-1-1-10-2001100
χ1222-12-22-1-1-1-21110000−i3i30022-12-22-1-1-1-21110000−i3i30022-12-22-1-1-1-21110000−i3i300
χ1322-12-22-1-1-1-21110000i3−i30022-12-22-1-1-1-21110000i3−i30022-12-22-1-1-1-21110000i3−i300
χ142-2220-2-22-20000000000−i2i22-2220-2-22-20000000000−i2i22-2220-2-22-20000000000−i2i2
χ152-2220-2-22-20000000000i2−i22-2220-2-22-20000000000i2−i22-2220-2-22-20000000000i2−i2
χ1644-2-24-2-211-2-2110000000044-2-24-2-211-2-2110000000044-2-24-2-211-2-21100000000
χ1744-2-2-4-2-21122-1-10000000044-2-2-4-2-21122-1-10000000044-2-2-4-2-21122-1-100000000
χ184-44-202-4-220000000000004-44-202-4-220000000000004-44-202-4-22000000000000
χ194-4-240-42-220000000000004-4-240-42-220000000000004-4-240-42-22000000000000
χ204-4-2-20221-1003i−3i000000004-4-2-20221-1003i−3i000000004-4-2-20221-1003i−3i00000000
χ214-4-2-20221-100−3i3i000000004-4-2-20221-100−3i3i000000004-4-2-20221-100−3i3i00000000
χ22111111111111111111111−1+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
χ2311111111111111-111-1-1-1-1−1+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+i321−i32−1+i32−1+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−i321+i32−1−i32−1−i321+i321+i321+i321+i32
χ241111111111111-11-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+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−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ251111111111111-1-1-1-1-1-111−1+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−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ262222-22222-2-2-2-200000000−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i300000000−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i300000000
χ27222-12-12-1-1-12-1-120-1-10000−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i32−1+i31−i321−i32−1+i301−i321−i320000−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i32−1−i31+i321+i32−1−i301+i321+i320000
χ28222-12-12-1-1-12-1-1-20110000−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i32−1+i31−i321−i321−i30−1+i32−1+i320000−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i32−1−i31+i321+i321+i30−1−i32−1−i320000
χ29222-1-2-12-1-11-21100−i3i30000−1+i3−1+i3−1+i31−i321−i31−i32−1+i31−i321−i32−1+i321−i3−1+i32−1+i32003+i32−3−i320000−1−i3−1−i3−1−i31+i321+i31+i32−1−i31+i321+i32−1−i321+i3−1−i32−1−i3200−3+i323−i320000
χ30222-1-2-12-1-11-21100i3−i30000−1+i3−1+i3−1+i31−i321−i31−i32−1+i31−i321−i32−1+i321−i3−1+i32−1+i3200−3−i323+i320000−1−i3−1−i3−1−i31+i321+i31+i32−1−i31+i321+i32−1−i321+i3−1−i32−1−i32003−i32−3+i320000
χ3122-1222-1-1-12-1-1-10200-1-100−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i320−1+i3001−i321−i3200−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i320−1−i3001+i321+i3200
χ3222-1222-1-1-12-1-1-10-2001100−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i3201−i300−1+i32−1+i3200−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i3201+i300−1−i32−1−i3200
χ3322-12-22-1-1-1-21110000−i3i300−1+i3−1+i31−i32−1+i31−i3−1+i31−i321−i321−i321−i3−1+i32−1+i32−1+i3200003+i32−3−i3200−1−i3−1−i31+i32−1−i31+i3−1−i31+i321+i321+i321+i3−1−i32−1−i32−1−i320000−3+i323−i3200
χ3422-12-22-1-1-1-21110000i3−i300−1+i3−1+i31−i32−1+i31−i3−1+i31−i321−i321−i321−i3−1+i32−1+i32−1+i320000−3−i323+i3200−1−i3−1−i31+i32−1−i31+i3−1−i31+i321+i321+i321+i3−1−i32−1−i32−1−i3200003−i32−3+i3200
χ352-2220-2-22-20000000000−i2i2−1+i31−i3−1+i3−1+i301−i31−i3−1+i31−i30000000000ζ5+ζ23−ζ5−ζ23−1−i31+i3−1−i3−1−i301+i31+i3−1−i31+i30000000000ζ7+ζ13−ζ7−ζ13
χ362-2220-2-22-20000000000i2−i2−1+i31−i3−1+i3−1+i301−i31−i3−1+i31−i30000000000−ζ5−ζ23ζ5+ζ23−1−i31+i3−1−i3−1−i301+i31+i3−1−i31+i30000000000−ζ7−ζ13ζ7+ζ13
χ3744-2-24-2-211-2-21100000000−2+2i3−2+2i31−i31−i3−2+2i31−i31−i3−1+i32−1+i321−i31−i3−1+i32−1+i3200000000−2−2i3−2−2i31+i31+i3−2−2i31+i31+i3−1−i32−1−i321+i31+i3−1−i32−1−i3200000000
χ3844-2-2-4-2-21122-1-100000000−2+2i3−2+2i31−i31−i32−2i31−i31−i3−1+i32−1+i32−1+i3−1+i31−i321−i3200000000−2−2i3−2−2i31+i31+i32+2i31+i31+i3−1−i32−1−i32−1−i3−1−i31+i321+i3200000000
χ394-44-202-4-22000000000000−2+2i32−2i3−2+2i31−i30−1+i32−2i31−i3−1+i3000000000000−2−2i32+2i3−2−2i31+i30−1−i32+2i31+i3−1−i3000000000000
χ404-4-240-42-22000000000000−2+2i32−2i31−i3−2+2i302−2i3−1+i31−i3−1+i3000000000000−2−2i32+2i31+i3−2−2i302+2i3−1−i31+i3−1−i3000000000000
χ414-4-2-20221-1003i−3i00000000−2+2i32−2i31−i31−i30−1+i3−1+i3−1+i321−i32003ζ14−3ζ1400000000−2−2i32+2i31+i31+i30−1−i3−1−i3−1−i321+i32003ζ22−3ζ2200000000
χ424-4-2-20221-100−3i3i00000000−2+2i32−2i31−i31−i30−1+i3−1+i3−1+i321−i3200−3ζ143ζ1400000000−2−2i32+2i31+i31+i30−1−i3−1−i3−1−i321+i3200−3ζ223ζ2200000000
χ43111111111111111111111−1−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
χ4411111111111111-111-1-1-1-1−1−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−i321+i32−1−i32−1−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+i321−i32−1+i32−1+i321−i321−i321−i321−i32
χ451111111111111-11-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−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+i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ461111111111111-1-1-1-1-1-111−1−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+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ472222-22222-2-2-2-200000000−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i300000000−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i300000000
χ48222-12-12-1-1-12-1-120-1-10000−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i32−1−i31+i321+i32−1−i301+i321+i320000−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i32−1+i31−i321−i32−1+i301−i321−i320000
χ49222-12-12-1-1-12-1-1-20110000−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i32−1−i31+i321+i321+i30−1−i32−1−i320000−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i32−1+i31−i321−i321−i30−1+i32−1+i320000
χ50222-1-2-12-1-11-21100−i3i30000−1−i3−1−i3−1−i31+i321+i31+i32−1−i31+i321+i32−1−i321+i3−1−i32−1−i3200−3+i323−i320000−1+i3−1+i3−1+i31−i321−i31−i32−1+i31−i321−i32−1+i321−i3−1+i32−1+i32003+i32−3−i320000
χ51222-1-2-12-1-11-21100i3−i30000−1−i3−1−i3−1−i31+i321+i31+i32−1−i31+i321+i32−1−i321+i3−1−i32−1−i32003−i32−3+i320000−1+i3−1+i3−1+i31−i321−i31−i32−1+i31−i321−i32−1+i321−i3−1+i32−1+i3200−3−i323+i320000
χ5222-1222-1-1-12-1-1-10200-1-100−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i320−1−i3001+i321+i3200−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i320−1+i3001−i321−i3200
χ5322-1222-1-1-12-1-1-10-2001100−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i3201+i300−1−i32−1−i3200−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i3201−i300−1+i32−1+i3200
χ5422-12-22-1-1-1-21110000−i3i300−1−i3−1−i31+i32−1−i31+i3−1−i31+i321+i321+i321+i3−1−i32−1−i32−1−i320000−3+i323−i3200−1+i3−1+i31−i32−1+i31−i3−1+i31−i321−i321−i321−i3−1+i32−1+i32−1+i3200003+i32−3−i3200
χ5522-12-22-1-1-1-21110000i3−i300−1−i3−1−i31+i32−1−i31+i3−1−i31+i321+i321+i321+i3−1−i32−1−i32−1−i3200003−i32−3+i3200−1+i3−1+i31−i32−1+i31−i3−1+i31−i321−i321−i321−i3−1+i32−1+i32−1+i320000−3−i323+i3200
χ562-2220-2-22-20000000000−i2i2−1−i31+i3−1−i3−1−i301+i31+i3−1−i31+i30000000000ζ7+ζ13−ζ7−ζ13−1+i31−i3−1+i3−1+i301−i31−i3−1+i31−i30000000000ζ5+ζ23−ζ5−ζ23
χ572-2220-2-22-20000000000i2−i2−1−i31+i3−1−i3−1−i301+i31+i3−1−i31+i30000000000−ζ7−ζ13ζ7+ζ13−1+i31−i3−1+i3−1+i301−i31−i3−1+i31−i30000000000−ζ5−ζ23ζ5+ζ23
χ5844-2-24-2-211-2-21100000000−2−2i3−2−2i31+i31+i3−2−2i31+i31+i3−1−i32−1−i321+i31+i3−1−i32−1−i3200000000−2+2i3−2+2i31−i31−i3−2+2i31−i31−i3−1+i32−1+i321−i31−i3−1+i32−1+i3200000000
χ5944-2-2-4-2-21122-1-100000000−2−2i3−2−2i31+i31+i32+2i31+i31+i3−1−i32−1−i32−1−i3−1−i31+i321+i3200000000−2+2i3−2+2i31−i31−i32−2i31−i31−i3−1+i32−1+i32−1+i3−1+i31−i321−i3200000000
χ604-44-202-4-22000000000000−2−2i32+2i3−2−2i31+i30−1−i32+2i31+i3−1−i3000000000000−2+2i32−2i3−2+2i31−i30−1+i32−2i31−i3−1+i3000000000000
χ614-4-240-42-22000000000000−2−2i32+2i31+i3−2−2i302+2i3−1−i31+i3−1−i3000000000000−2+2i32−2i31−i3−2+2i302−2i3−1+i31−i3−1+i3000000000000
χ624-4-2-20221-1003i−3i00000000−2−2i32+2i31+i31+i30−1−i3−1−i3−1−i321+i32003ζ22−3ζ2200000000−2+2i32−2i31−i31−i30−1+i3−1+i3−1+i321−i32003ζ14−3ζ1400000000
χ634-4-2-20221-100−3i3i00000000−2−2i32+2i31+i31+i30−1−i3−1−i3−1−i321+i3200−3ζ223ζ2200000000−2+2i32−2i31−i31−i30−1+i3−1+i3−1+i321−i3200−3ζ143ζ1400000000

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