Finite Group Databasebeta

← Group #11771628

Character table — Group #11771628

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size1111222222222222222222222222222222222244444444444444444444444444444444444444444444444444444412121212121212121212121212121212121212121212121224242424242424242424242472727272
order122233444444666666888812121212121212122424242424242424366688121212121212121212121212121212121212121224242424242424242424242424242424242424242424242424242424161616161616161648484848484848484848484848484848444412121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1ii−i−i
χ6111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-11111−i−iii
χ7111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−i−iii
χ8111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-11111ii−i−i
χ91-11-111i−i1-1i−i1-1-1-11-1ii−i−iii−i−i11-1-1iiii−i−i−i−i11-1-11-1ii−i−ii−iiiii−i−i−i−i1-111-1-111-1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ131-1i−i11-1-1ii−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ101-11-111i−i1-1i−i1-1-1-11-1ii−i−iii−i−i11-1-1iiii−i−i−i−i11-1-11-1ii−i−ii−iiiii−i−i−i−i1-111-1-111-1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13-11−ii-1-111−i−iii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ111-11-111i−i1-1i−i1-1-1-11-1ii−i−iii−i−i11-1-1iiii−i−i−i−i11-1-11-1ii−i−ii−iiiii−i−i−i−i1-111-1-111-1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ131-1i−i11-1-1ii−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ121-11-111i−i1-1i−i1-1-1-11-1ii−i−iii−i−i11-1-1iiii−i−i−i−i11-1-11-1ii−i−ii−iiiii−i−i−i−i1-111-1-111-1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13-11−ii-1-111−i−iiiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ131-11-111−ii1-1−ii1-1-1-11-1−i−iii−i−iii11-1-1−i−i−i−iiiii11-1-11-1−i−iii−ii−i−i−i−iiiii1-111-1-111-1-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ231-1−ii11-1-1−i−iii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ141-11-111−ii1-1−ii1-1-1-11-1−i−iii−i−iii11-1-1−i−i−i−iiiii11-1-11-1−i−iii−ii−i−i−i−iiiii1-111-1-111-1-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23-11i−i-1-111ii−i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ151-11-111−ii1-1−ii1-1-1-11-1−i−iii−i−iii11-1-1−i−i−i−iiiii11-1-11-1−i−iii−ii−i−i−i−iiiii1-111-1-111-1-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ231-1−ii11-1-1−i−iiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ161-11-111−ii1-1−ii1-1-1-11-1−i−iii−i−iii11-1-1−i−i−i−iiiii11-1-11-1−i−iii−ii−i−i−i−iiiii1-111-1-111-1-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23-11i−i-1-111ii−i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ17222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ1822222222-2-2-2-222222200002222-2-2-2-2000000002222002-22-2-2-222-2-222-2-2-2-2-2-2-2-20000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ1922222222-2-2-2-222222200002222-2-2-2-2000000002222002-22-2-2-222-2-222-2-2-2-2-2-2-2-20000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ20222222-2-222-2-22222222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222220000000000000000000000000000000000000000
χ21222222-2-2-2-2222222220000-2-2-2-2-2-2-2-200000000222200-22-2222-2-222-2-222-2-2-2-2-2-200000000000000000000000000002−22−2−22−2222−2−222−2−2−2−222−2−2220000000000000000
χ22222222-2-2-2-2222222220000-2-2-2-2-2-2-2-200000000222200-22-2222-2-222-2-222-2-2-2-2-2-20000000000000000000000000000−22−222−22−2−2−222−2−22222−2−222−2−20000000000000000
χ2322222-1222222222-1-1-12222-1-1-1-1222222222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002222-1-1-1-1-1-1-1-10000
χ2422222-1222222222-1-1-12222-1-1-1-1222222222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-2111111110000
χ2522222-1222222222-1-1-1-2-2-2-2-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111111111110000000000000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2622222-1222222222-1-1-1-2-2-2-2-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111111111110000000000000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2722222-1-2-222-2-2222-1-1-122221111222222222222-1-1-1-1-2-2-2-2-2-21111111111-1-1-1-1-1-1-2-2-2-2111111111111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ2822222-1-2-222-2-2222-1-1-122221111222222222222-1-1-1-1-2-2-2-2-2-21111111111-1-1-1-1-1-1-2-2-2-2111111111111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ2922222-1-2-222-2-2222-1-1-1-2-2-2-211112222-2-2-2-2-2-2-2-2-1-1-1-122-2-2-2-21111111111-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000000000000022-2-2-1-1-1-111110000
χ3022222-1-2-222-2-2222-1-1-1-2-2-2-211112222-2-2-2-2-2-2-2-2-1-1-1-122-2-2-2-21111111111-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-2-2221111-1-1-1-10000
χ312222-12222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ322222-12222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ332222-12222222-1-1-1222-2-2-2-22222-1-1-1-111111111-1-1-1-1-2-2-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-21111-2-21111-2-21111-2-21111000000003−33−33−33−33−33−33−33−30000000000000000
χ342222-12222222-1-1-1222-2-2-2-22222-1-1-1-111111111-1-1-1-1-2-2-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-21111-2-21111-2-21111-2-2111100000000−33−33−33−33−33−33−33−330000000000000000
χ352222-1222-2-2-2-2-1-1-122200002222111133−3−333−3−3-1-1-1-100-11-11-2-2-1-111-1-111-2-211113−33−30033−3−30033−3−30033−3−30033−3−3−i2i2−i2i2−i2i2−i2i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ362222-1222-2-2-2-2-1-1-122200002222111133−3−333−3−3-1-1-1-100-11-11-2-2-1-111-1-111-2-211113−33−30033−3−30033−3−30033−3−30033−3−3i2−i2i2−i2i2−i2i2−i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ372222-1222-2-2-2-2-1-1-1222000022221111−3−333−3−333-1-1-1-100-11-11-2-2-1-111-1-111-2-21111−33−3300−3−33300−3−33300−3−33300−3−333−i2i2−i2i2−i2i2−i2i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ382222-1222-2-2-2-2-1-1-1222000022221111−3−333−3−333-1-1-1-100-11-11-2-2-1-111-1-111-2-21111−33−3300−3−33300−3−33300−3−33300−3−333i2−i2i2−i2i2−i2i2−i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ392222-12-2-222-2-2-1-1-12222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-21111111122-1-1-1-11111-2-21111-2-2111122-1-1-1-122-1-1-1-100000000−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ402222-12-2-222-2-2-1-1-12222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-21111111122-1-1-1-11111-2-21111-2-2111122-1-1-1-122-1-1-1-100000000i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ412222-12-2-222-2-2-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-1221111-2-21111111122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-21111-2-211112i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii0000000000000000
χ422222-12-2-222-2-2-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-1221111-2-21111111122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-21111-2-21111−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i0000000000000000
χ432222-12-2-2-2-222-1-1-12220000-2-2-2-2111133−3−333−3−3-1-1-1-1001-11-12211-1-111-1-1-2-21111−33−3300−3−33300−3−3330033−3−30033−3−32−22−2−22−22ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000000000
χ442222-12-2-2-2-222-1-1-12220000-2-2-2-2111133−3−333−3−3-1-1-1-1001-11-12211-1-111-1-1-2-21111−33−3300−3−33300−3−3330033−3−30033−3−3−22−222−22−2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ452222-12-2-2-2-222-1-1-12220000-2-2-2-21111−3−333−3−333-1-1-1-1001-11-12211-1-111-1-1-2-211113−33−30033−3−30033−3−300−3−33300−3−3332−22−2−22−22ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ462222-12-2-2-2-222-1-1-12220000-2-2-2-21111−3−333−3−333-1-1-1-1001-11-12211-1-111-1-1-2-211113−33−30033−3−30033−3−300−3−33300−3−333−22−222−22−2−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.