Finite Group Databasebeta

← Group #72268781

Character table — Group #72268781

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size11111111333333334444441212121212121212121212121212121212121212121212121212121212121212121212121212161616161616161616161616161616161616161616161616484848484848484864646464646464646464646464646464646464646464646464646464
order1222222222222222444444444444444444444444444444444444444444442222223344666666666666662244444466666666666612121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111−1−i32−1+i3211−1−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+i3211111111−1−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
χ3111111111111111111111111111111111111111111111111111111111111111111−1+i32−1−i3211−1+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−i3211111111−1+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
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1
χ5111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1−1−i32−1+i32-1-1−1−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+i32-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ6111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1−1+i32−1−i32-1-1−1+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−i32-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ7111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111111111111-1-11111-1-11111-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1
χ8111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−1−i32−1+i32-1-1−1−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+i32-1-11111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32
χ9111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−1+i32−1−i32-1-1−1+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−i32-1-11111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32
χ10111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ11111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−1−i32−1+i3211−1−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+i3211-1-1-1-1111+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ12111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−1+i32−1−i3211−1+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−i3211-1-1-1-1111−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ131111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111111111111111-1-111-1-11111-1-11111-1-111-1-111-1-1-1-1-1-111-1-1-1-1
χ141111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111−1−i32−1+i32-1-1−1−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+i32-1-111-1-111−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32
χ151111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111−1+i32−1−i32-1-1−1+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−i32-1-111-1-111−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32
χ161111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111111111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ171111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1−1−i32−1+i3211−1−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+i3211-1-111-1-11+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ181111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1−1+i32−1−i3211−1+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−i3211-1-111-1-11−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ191111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ201111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−1−i32−1+i3211−1−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+i321111-1-1-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ211111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−1+i32−1−i3211−1+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−i321111-1-1-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ221111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-1-1-1-1-111-1-1
χ231111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111−1−i32−1+i32-1-1−1−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+i32-1-1-1-111111+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32
χ241111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111−1+i32−1−i32-1-1−1+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−i32-1-1-1-111111−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ2522-2-22-2-2222-2-222-2-200002-200002-22222-2-2-2-200000000000000002222-2-2-2-200000022002-2-22-2-222-2-222-2-20000000000000000000000002-20000002-200
χ2622-2-22-2-2222-2-222-2-200002-200002-22222-2-2-2-200000000000000002222-2-2-2-2000000−1−i3−1+i300−1−i31+i31+i3−1+i31−i31−i3−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3000000000000000000000000−1−i31+i3000000−1+i31−i300
χ2722-2-22-2-2222-2-222-2-200002-200002-22222-2-2-2-200000000000000002222-2-2-2-2000000−1+i3−1−i300−1+i31−i31−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i3000000000000000000000000−1+i31−i3000000−1−i31+i300
χ2822-2-22-2-2222-2-222-2-20000-220000-222222-2-2-2-20000000000000000-2-2-2-2222200000022002-2-22-2-222-2-222-2-2000000000000000000000000-22000000-2200
χ2922-2-22-2-2222-2-222-2-20000-220000-222222-2-2-2-20000000000000000-2-2-2-22222000000−1−i3−1+i300−1−i31+i31+i3−1+i31−i31−i3−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i30000000000000000000000001+i3−1−i30000001−i3−1+i300
χ3022-2-22-2-2222-2-222-2-20000-220000-222222-2-2-2-20000000000000000-2-2-2-22222000000−1+i3−1−i300−1+i31−i31−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i30000000000000000000000001−i3−1+i30000001+i3−1−i300
χ312-22-2-22-222-22-22-22-2002-200002-20022-2-222-2-2000000002222-2-2-2-2000000000000002200-22-2-22-22-22-22-22-200000000000000000000002-20000002-20000
χ322-22-2-22-222-22-22-22-2002-200002-20022-2-222-2-2000000002222-2-2-2-200000000000000−1−i3−1+i3001+i3−1−i31+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i30000000000000000000000−1−i31+i3000000−1+i31−i30000
χ332-22-2-22-222-22-22-22-2002-200002-20022-2-222-2-2000000002222-2-2-2-200000000000000−1+i3−1−i3001−i3−1+i31−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i30000000000000000000000−1+i31−i3000000−1−i31+i30000
χ342-22-2-22-222-22-22-22-200-220000-220022-2-222-2-200000000-2-2-2-22222000000000000002200-22-2-22-22-22-22-22-20000000000000000000000-22000000-220000
χ352-22-2-22-222-22-22-22-200-220000-220022-2-222-2-200000000-2-2-2-2222200000000000000−1−i3−1+i3001+i3−1−i31+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i300000000000000000000001+i3−1−i30000001−i3−1+i30000
χ362-22-2-22-222-22-22-22-200-220000-220022-2-222-2-200000000-2-2-2-2222200000000000000−1+i3−1−i3001−i3−1+i31−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i300000000000000000000001−i3−1+i30000001+i3−1−i30000
χ372-2-22-2-2222-2-222-2-222-200002-2000022-2-2-2-2222222-2-2-2-200000000000000000000002200-2-22-2-222-2-222-2-22000000000000000000002-20000002-2000000
χ382-2-22-2-2222-2-222-2-222-200002-2000022-2-2-2-2222222-2-2-2-20000000000000000000000−1−i3−1+i3001+i31+i3−1−i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i300000000000000000000−1−i31+i3000000−1+i31−i3000000
χ392-2-22-2-2222-2-222-2-222-200002-2000022-2-2-2-2222222-2-2-2-20000000000000000000000−1+i3−1−i3001−i31−i3−1+i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i300000000000000000000−1+i31−i3000000−1−i31+i3000000
χ402-2-22-2-2222-2-222-2-22-220000-22000022-2-2-2-222-2-2-2-2222200000000000000000000002200-2-22-2-222-2-222-2-2200000000000000000000-22000000-22000000
χ412-2-22-2-2222-2-222-2-22-220000-22000022-2-2-2-222-2-2-2-222220000000000000000000000−1−i3−1+i3001+i31+i3−1−i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3000000000000000000001+i3−1−i30000001−i3−1+i3000000
χ422-2-22-2-2222-2-222-2-22-220000-22000022-2-2-2-222-2-2-2-222220000000000000000000000−1+i3−1−i3001−i31−i3−1+i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3000000000000000000001−i3−1+i30000001+i3−1−i3000000
χ433333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333333003300000000000000-1-1-1-1-1-1-1-10000000000000000000000000000
χ443333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-3-3-300-3-300000000000000111111110000000000000000000000000000
χ45333333333333333333-3-3-3-333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111113333-3-300-3-30000000000000011-1-1-1-1110000000000000000000000000000
χ46333333333333333333-3-3-3-333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-3-3-3-333003300000000000000-1-11111-1-10000000000000000000000000000
χ473333333333333333-3-333-3-3-3-333-3-3-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111133-3-33300-3-30000000000000011-1-111-1-10000000000000000000000000000
χ483333333333333333-3-333-3-3-3-333-3-3-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-3-333-3-3003300000000000000-1-111-1-1110000000000000000000000000000
χ493333333333333333-3-3-3-333-3-3-3-333-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-133-3-3-3-3003300000000000000-1-1-1-111110000000000000000000000000000
χ503333333333333333-3-3-3-333-3-3-3-333-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-3-3333300-3-3000000000000001111-1-1-1-10000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.