Finite Group Databasebeta

← Group #72227312

Character table — Group #72227312

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size112224466666666661212121212121212121212121212121616161632323232323264646464112224466666666661212121212121212121212121212121616161632323232323264646464
order12488222222244444222222444488888336612122424242466662248822222224444422222244448888866661212242424246666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111−1−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+i3211111111111111111111111111111111−1−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
χ311111111111111111111111111111111−1+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−i3211111111111111111111111111111111−1+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
χ411111-1-11111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1
χ511111-1-11111111111-1-1-1-1-1-1-1-1-1-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211111-1-11111111111-1-1-1-1-1-1-1-1-1-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ611111-1-11111111111-1-1-1-1-1-1-1-1-1-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211111-1-11111111111-1-1-1-1-1-1-1-1-1-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ7111-1-11-11111111111111-1-1-111-1-1-1-1-1-1-1111111-1-1-1-11-11-1111-1-11-11111111111111-1-1-111-1-1-1-1-1-1-1111111-1-1-1-11-11-1
χ8111-1-11-11111111111111-1-1-111-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i321+i32−1+i321−i32111-1-11-11111111111111-1-1-111-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i321+i32−1+i321−i32
χ9111-1-11-11111111111111-1-1-111-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i321−i32−1−i321+i32111-1-11-11111111111111-1-1-111-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i321−i32−1−i321+i32
χ10111-1-1-111111111111-1-1-1111-1-111-1-1-1-1-1111111-1-1-1-1-11-11111-1-1-111111111111-1-1-1111-1-111-1-1-1-1-1111111-1-1-1-1-11-11
χ11111-1-1-111111111111-1-1-1111-1-111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i32−1−i321−i32−1+i32111-1-1-111111111111-1-1-1111-1-111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i32−1−i321−i32−1+i32
χ12111-1-1-111111111111-1-1-1111-1-111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i32−1+i321+i32−1−i32111-1-1-111111111111-1-1-1111-1-111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i32−1+i321+i32−1−i32
χ1322-20000222-2-222-2-2-20000000000000002222-2-20000000022-20000222-2-222-2-2-20000000000000002222-2-200000000
χ1422-20000222-2-222-2-2-2000000000000000−1−i3−1+i3−1−i3−1+i31+i31−i30000000022-20000222-2-222-2-2-2000000000000000−1−i3−1+i3−1−i3−1+i31+i31−i300000000
χ1522-20000222-2-222-2-2-2000000000000000−1+i3−1−i3−1+i3−1−i31−i31+i30000000022-20000222-2-222-2-2-2000000000000000−1+i3−1−i3−1+i3−1−i31−i31+i300000000
χ1633333333-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-10000000000000033333333-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-100000000000000
χ173333333-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1000000000000003333333-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-13-1-1-100000000000000
χ183333333-1-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-13-1-1000000000000003333333-1-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-13-1-100000000000000
χ193333333-1-1-13-13-1-1-1-1-1-1-1-1-1-13-13-1-1-1-13-1000000000000003333333-1-1-13-13-1-1-1-1-1-1-1-1-1-13-13-1-1-1-13-100000000000000
χ203333333-1-1-1-13-13-1-1-1-1-1-1-1-1-1-13-13-1-1-1-13000000000000003333333-1-1-1-13-13-1-1-1-1-1-1-1-1-1-13-13-1-1-1-1300000000000000
χ2133333-3-33-1-1-1-1-1-13-1-1-311-31111113-1-1-1-10000000000000033333-3-33-1-1-1-1-1-13-1-1-311-31111113-1-1-1-100000000000000
χ2233333-3-3-13-1-1-1-1-1-13-11-311-311111-13-1-1-10000000000000033333-3-3-13-1-1-1-1-1-13-11-311-311111-13-1-1-100000000000000
χ2333333-3-3-1-13-1-1-1-1-1-1311-311-31111-1-13-1-10000000000000033333-3-3-1-13-1-1-1-1-1-1311-311-31111-1-13-1-100000000000000
χ2433333-3-3-1-1-13-13-1-1-1-1111111-31-31-1-1-13-10000000000000033333-3-3-1-1-13-13-1-1-1-1111111-31-31-1-1-13-100000000000000
χ2533333-3-3-1-1-1-13-13-1-1-11111111-31-3-1-1-1-130000000000000033333-3-3-1-1-1-13-13-1-1-11111111-31-3-1-1-1-1300000000000000
χ26333-3-33-33-1-1-1-1-1-13-1-13-1-1-311-1-111-3111100000000000000333-3-33-33-1-1-1-1-1-13-1-13-1-1-311-1-111-3111100000000000000
χ27333-3-33-3-13-1-1-1-1-1-13-1-13-11-31-1-1111-311100000000000000333-3-33-3-13-1-1-1-1-1-13-1-13-11-31-1-1111-311100000000000000
χ28333-3-33-3-1-13-1-1-1-1-1-13-1-1311-3-1-11111-31100000000000000333-3-33-3-1-13-1-1-1-1-1-13-1-1311-3-1-11111-31100000000000000
χ29333-3-33-3-1-1-13-13-1-1-1-1-1-1-11113-1-31111-3100000000000000333-3-33-3-1-1-13-13-1-1-1-1-1-1-11113-1-31111-3100000000000000
χ30333-3-33-3-1-1-1-13-13-1-1-1-1-1-1111-131-31111-300000000000000333-3-33-3-1-1-1-13-13-1-1-1-1-1-1111-131-31111-300000000000000
χ31333-3-3-333-1-1-1-1-1-13-1-1-3113-1-111-1-1-3111100000000000000333-3-3-333-1-1-1-1-1-13-1-1-3113-1-111-1-1-3111100000000000000
χ32333-3-3-33-13-1-1-1-1-1-13-11-31-13-111-1-11-311100000000000000333-3-3-33-13-1-1-1-1-1-13-11-31-13-111-1-11-311100000000000000
χ33333-3-3-33-1-13-1-1-1-1-1-1311-3-1-1311-1-111-31100000000000000333-3-3-33-1-13-1-1-1-1-1-1311-3-1-1311-1-111-31100000000000000
χ34333-3-3-33-1-1-13-13-1-1-1-1111-1-1-1-313-1111-3100000000000000333-3-3-33-1-1-13-13-1-1-1-1111-1-1-1-313-1111-3100000000000000
χ35333-3-3-33-1-1-1-13-13-1-1-1111-1-1-11-3-131111-300000000000000333-3-3-33-1-1-1-13-13-1-1-1111-1-1-11-3-131111-300000000000000
χ3666-600006-2-222-2-2-6220000000000000000000000000000066-600006-2-222-2-2-62200000000000000000000000000000
χ3766-60000-26-222-2-22-620000000000000000000000000000066-60000-26-222-2-22-6200000000000000000000000000000
χ3866-60000-2-2622-2-222-60000000000000000000000000000066-60000-2-2622-2-222-600000000000000000000000000000
χ3966-60000-2-2-22-6-262220000000000000000000000000000066-60000-2-2-22-6-2622200000000000000000000000000000
χ4066-60000-2-2-2-626-22220000000000000000000000000000066-60000-2-2-2-626-222200000000000000000000000000000
χ418-8042−4200000000000000000000000000022-2-2002−22−200008-8042−4200000000000000000000000000022-2-2002−22−20000
χ428-8042−42000000000000000000000000000−1−i3−1+i31+i31−i300−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ2300008-8042−42000000000000000000000000000−1−i3−1+i31+i31−i300−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000
χ438-8042−42000000000000000000000000000−1+i3−1−i31−i31+i300ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ1300008-8042−42000000000000000000000000000−1+i3−1−i31−i31+i300ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000
χ448-80−424200000000000000000000000000022-2-200−22−2200008-80−424200000000000000000000000000022-2-200−22−220000
χ458-80−4242000000000000000000000000000−1−i3−1+i31+i31−i300ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ2300008-80−4242000000000000000000000000000−1−i3−1+i31+i31−i300ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000
χ468-80−4242000000000000000000000000000−1+i3−1−i31−i31+i300−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ1300008-80−4242000000000000000000000000000−1+i3−1−i31−i31+i300−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4811111111111111111111111111111111−1−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+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i32
χ4911111111111111111111111111111111−1+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−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321−i321+i321+i321−i321−i321+i321+i32
χ5011111-1-11111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-11111111111-1-1-1-1-1-1-1-1-1-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ5211111-1-11111111111-1-1-1-1-1-1-1-1-1-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ53111-1-11-11111111111111-1-1-111-1-1-1-1-1-1-1111111-1-1-1-11-11-1-1-1-111-11-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-11111-11-11
χ54111-1-11-11111111111111-1-1-111-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i321+i32−1+i321−i32-1-1-111-11-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111111+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i32
χ55111-1-11-11111111111111-1-1-111-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i321−i32−1−i321+i32-1-1-111-11-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111111−i321+i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i32
χ56111-1-1-111111111111-1-1-1111-1-111-1-1-1-1-1111111-1-1-1-1-11-11-1-1-1111-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-111111-1-1-1-1-1-111111-11-1
χ57111-1-1-111111111111-1-1-1111-1-111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i32−1−i321−i32−1+i32-1-1-1111-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1111111+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i32
χ58111-1-1-111111111111-1-1-1111-1-111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i32−1+i321+i32−1−i32-1-1-1111-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1111111−i321+i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i32
χ5922-20000222-2-222-2-2-20000000000000002222-2-200000000-2-220000-2-2-222-2-2222000000000000000-2-2-2-22200000000
χ6022-20000222-2-222-2-2-2000000000000000−1−i3−1+i3−1−i3−1+i31+i31−i300000000-2-220000-2-2-222-2-22220000000000000001+i31−i31+i31−i3−1−i3−1+i300000000
χ6122-20000222-2-222-2-2-2000000000000000−1+i3−1−i3−1+i3−1−i31−i31+i300000000-2-220000-2-2-222-2-22220000000000000001−i31+i31−i31+i3−1+i3−1−i300000000
χ6233333333-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-100000000000000-3-3-3-3-3-3-3-3111111-311-311-3111111-3111100000000000000
χ633333333-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-13-1-1-100000000000000-3-3-3-3-3-3-31-3111111-311-311-3111111-311100000000000000
χ643333333-1-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-13-1-100000000000000-3-3-3-3-3-3-311-3111111-311-311-3111111-31100000000000000
χ653333333-1-1-13-13-1-1-1-1-1-1-1-1-1-13-13-1-1-1-13-100000000000000-3-3-3-3-3-3-3111-31-31111111111-31-31111-3100000000000000
χ663333333-1-1-1-13-13-1-1-1-1-1-1-1-1-1-13-13-1-1-1-1300000000000000-3-3-3-3-3-3-31111-31-31111111111-31-31111-300000000000000
χ6733333-3-33-1-1-1-1-1-13-1-1-311-31111113-1-1-1-100000000000000-3-3-3-3-333-3111111-3113-1-13-1-1-1-1-1-1-3111100000000000000
χ6833333-3-3-13-1-1-1-1-1-13-11-311-311111-13-1-1-100000000000000-3-3-3-3-3331-3111111-31-13-1-13-1-1-1-1-11-311100000000000000
χ6933333-3-3-1-13-1-1-1-1-1-1311-311-31111-1-13-1-100000000000000-3-3-3-3-33311-3111111-3-1-13-1-13-1-1-1-111-31100000000000000
χ7033333-3-3-1-1-13-13-1-1-1-1111111-31-31-1-1-13-100000000000000-3-3-3-3-333111-31-31111-1-1-1-1-1-13-13-1111-3100000000000000
χ7133333-3-3-1-1-1-13-13-1-1-11111111-31-3-1-1-1-1300000000000000-3-3-3-3-3331111-31-3111-1-1-1-1-1-1-13-131111-300000000000000
χ72333-3-33-33-1-1-1-1-1-13-1-13-1-1-311-1-111-3111100000000000000-3-3-333-33-3111111-311-3113-1-111-1-13-1-1-1-100000000000000
χ73333-3-33-3-13-1-1-1-1-1-13-1-13-11-31-1-1111-311100000000000000-3-3-333-331-3111111-311-31-13-111-1-1-13-1-1-100000000000000
χ74333-3-33-3-1-13-1-1-1-1-1-13-1-1311-3-1-11111-31100000000000000-3-3-333-3311-3111111-311-3-1-1311-1-1-1-13-1-100000000000000
χ75333-3-33-3-1-1-13-13-1-1-1-1-1-1-11113-1-31111-3100000000000000-3-3-333-33111-31-31111111-1-1-1-313-1-1-1-13-100000000000000
χ76333-3-33-3-1-1-1-13-13-1-1-1-1-1-1111-131-31111-300000000000000-3-3-333-331111-31-3111111-1-1-11-3-13-1-1-1-1300000000000000
χ77333-3-3-333-1-1-1-1-1-13-1-1-3113-1-111-1-1-3111100000000000000-3-3-3333-3-3111111-3113-1-1-311-1-1113-1-1-1-100000000000000
χ78333-3-3-33-13-1-1-1-1-1-13-11-31-13-111-1-11-311100000000000000-3-3-3333-31-3111111-31-13-11-31-1-111-13-1-1-100000000000000
χ79333-3-3-33-1-13-1-1-1-1-1-1311-3-1-1311-1-111-31100000000000000-3-3-3333-311-3111111-3-1-1311-3-1-111-1-13-1-100000000000000
χ80333-3-3-33-1-1-13-13-1-1-1-1111-1-1-1-313-1111-3100000000000000-3-3-3333-3111-31-31111-1-1-11113-1-31-1-1-13-100000000000000
χ81333-3-3-33-1-1-1-13-13-1-1-1111-1-1-11-3-131111-300000000000000-3-3-3333-31111-31-3111-1-1-1111-131-3-1-1-1-1300000000000000
χ8266-600006-2-222-2-2-62200000000000000000000000000000-6-660000-622-2-2226-2-200000000000000000000000000000
χ8366-60000-26-222-2-22-6200000000000000000000000000000-6-6600002-62-2-222-26-200000000000000000000000000000
χ8466-60000-2-2622-2-222-600000000000000000000000000000-6-66000022-6-2-222-2-2600000000000000000000000000000
χ8566-60000-2-2-22-6-2622200000000000000000000000000000-6-660000222-262-6-2-2-200000000000000000000000000000
χ8666-60000-2-2-2-626-222200000000000000000000000000000-6-6600002226-2-62-2-2-200000000000000000000000000000
χ878-8042−4200000000000000000000000000022-2-2002−22−20000-880−4242000000000000000000000000000-2-22200−22−220000
χ888-8042−42000000000000000000000000000−1−i3−1+i31+i31−i300−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000-880−42420000000000000000000000000001+i31−i3−1−i3−1+i300ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000
χ898-8042−42000000000000000000000000000−1+i3−1−i31−i31+i300ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000-880−42420000000000000000000000000001−i31+i3−1+i3−1−i300−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000
χ908-80−424200000000000000000000000000022-2-200−22−220000-88042−42000000000000000000000000000-2-222002−22−20000
χ918-80−4242000000000000000000000000000−1−i3−1+i31+i31−i300ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230000-88042−420000000000000000000000000001+i31−i3−1−i3−1+i300−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230000
χ928-80−4242000000000000000000000000000−1+i3−1−i31−i31+i300−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130000-88042−420000000000000000000000000001−i31+i3−1+i3−1−i300ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130000

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