Finite Group Databasebeta

← Group #13155537

Character table — Group #13155537

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444466668888888812121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363654545454
order12224444333666666666121212121212121212121212333666666666121212121212121212121212888836661212121224666666668812121212121212122424242424242424242424242424242424242424242424242424242424242424888844881212121224242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-11-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i1-1i−i11-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-11-111111111−ii-1-1-1-1-1-1-1-1ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iii-11i−i-1-111ii−i−i−i−iii-1-111
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-1-11-1-1-1-1-1-1-1-1i−i11111111ii−i−iii−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii1-1−ii11-1-1−i−iii−i−iii-1-111
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-1-11-1-1-1-1-1-1-1-1−ii11111111ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i-11−ii-1-111−i−iiiii−i−i11-1-1
χ131111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1-1-11-111111111i−i-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i-11−ii-1-111−i−iiiii−i−i-1-111
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1-1-11-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii1-1−ii11-1-1−i−iii−i−iii11-1-1
χ151111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1-1-1-11-1-1-1-1-1-1-1-1i−i11111111−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii-11i−i-1-111ii−i−i−i−iii11-1-1
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1-1-1-11-1-1-1-1-1-1-1-1−ii11111111−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−i1-1i−i11-1-1ii−i−iii−i−i-1-111
χ172222222222-122-1-122-1222222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-10000-1-1-1-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-10000-1-1-1-10000222200000000-1-1-1-1-1-1-1-12222000000000000-1-1-1-10000
χ182222222222-122-1-122-1222222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-10000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-2-222-1-1-1-1-1-1000011110000-2-2-2-20000000011111111-2-2-2-200000000000011110000
χ192222222222-122-1-122-1222222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-10000-1-1-1-1-1-1-1-1-2-2-2-211111122-2-21111110000-1-1-1-10000222200000000-1-1-1-1-1-1-1-1-2-2-2-200000000000011110000
χ202222222222-122-1-122-1222222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-10000-1-1-1-1-1-1-1-1-2-2-2-2111111-2-2-2-2111111000011110000-2-2-2-200000000111111112222000000000000-1-1-1-10000
χ21222222222-12-1-1222-122222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-122-1-1-1-100-1-122-1-1-1-1-1-1-1-1000022220000-1-1-1-1-1-1-1-100000000000000220000-1-1-1-100000000
χ22222222222-12-1-1222-122222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-211-2-211110011-2-21111-1-1-1-1000022220000-1-1-1-1-1-1-1-100000000000000-2-20000111100000000
χ23222222222-12-1-1222-122222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-122-1-122-1-1-1-100-1-122-1-1-1-111110000-2-2-2-200001111111100000000000000-2-20000111100000000
χ24222222222-12-1-1222-122222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-211-2-211110011-2-2111111110000-2-2-2-200001111111100000000000000220000-1-1-1-100000000
χ2522222222-1222222-122-1-1-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-10000000000220000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100002200-1-1-1-1000000000000
χ2622222222-1222222-122-1-1-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-10000000000-2-2000000002222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111111110000-2-2001111000000000000
χ2722222222-1222222-122-1-1-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-100000000002200000000-2-2-2-222221111-1-1-1-111111111-1-1-1-1-1-1-1-10000-2-2001111000000000000
χ2822222222-1222222-122-1-1-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-10000000000-2-200000000-2-2-2-2-2-2-2-211111111111111111111111100002200-1-1-1-1000000000000
χ292222-2-2-2-222-122-1-122-122-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-2111111-2-2110000-1-1-1-111112-222-1-1-1-1-1-12i−2i-2-21111110000−i−iii00002i2i−2i−2i00000000−i−i−i−iiiii2i2i−2i−2i000000000000−i−iii0000
χ302222-2-2-2-222-122-1-122-122-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-2111111-2-2110000-1-1-1-111112-222-1-1-1-1-1-1−2i2i-2-21111110000ii−i−i0000−2i−2i2i2i00000000iiii−i−i−i−i−2i−2i2i2i000000000000ii−i−i0000
χ312222-2-2-2-222-122-1-122-122-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-2111111-2-2110000-1-1-1-11111-22-2-21111112i−2i22-1-1-1-1-1-10000−i−iii00002i2i−2i−2i00000000−i−i−i−iiiii−2i−2i2i2i000000000000ii−i−i0000
χ322222-2-2-2-222-122-1-122-122-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-2111111-2-2110000-1-1-1-11111-22-2-2111111−2i2i22-1-1-1-1-1-10000ii−i−i0000−2i−2i2i2i00000000iiii−i−i−i−i2i2i−2i−2i000000000000−i−iii0000
χ332222-2-2-2-22-12-1-1222-1222-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-2111111-2-22i2i−2i−2i-1-1-1-111112-2-1-122-1-1-1-10011-2-21111−i−iii00002i2i−2i−2i0000−i−i−i−iiiii000000000000002i−2i0000−i−iii00000000
χ342222-2-2-2-22-12-1-1222-1222-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-2111111-2-22i2i−2i−2i-1-1-1-11111-2211-2-2111100-1-122-1-1-1-1−i−iii00002i2i−2i−2i0000−i−i−i−iiiii00000000000000−2i2i0000ii−i−i00000000
χ352222-2-2-2-22-12-1-1222-1222-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-2111111-2-2−2i−2i2i2i-1-1-1-111112-2-1-122-1-1-1-10011-2-21111ii−i−i0000−2i−2i2i2i0000iiii−i−i−i−i00000000000000−2i2i0000ii−i−i00000000
χ362222-2-2-2-22-12-1-1222-1222-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-2111111-2-2−2i−2i2i2i-1-1-1-11111-2211-2-2111100-1-122-1-1-1-1ii−i−i0000−2i−2i2i2i0000iiii−i−i−i−i000000000000002i−2i0000−i−iii00000000
χ372222-2-2-2-2-1222222-122-1-111-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-211112i2i−2i−2i-1-1-1-1111100000000002i−2i000000002i2i−2i−2i2i2i−2i−2i−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii00002-200-1-111000000000000
χ382222-2-2-2-2-1222222-122-1-111-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-211112i2i−2i−2i-1-1-1-111110000000000−2i2i000000002i2i−2i−2i−2i−2i2i2i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i0000-220011-1-1000000000000
χ392222-2-2-2-2-1222222-122-1-111-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111−2i−2i2i2i-1-1-1-1111100000000002i−2i00000000−2i−2i2i2i2i2i−2i−2iii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii0000-220011-1-1000000000000
χ402222-2-2-2-2-1222222-122-1-111-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111−2i−2i2i2i-1-1-1-111110000000000−2i2i00000000−2i−2i2i2i−2i−2i2i2iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i00002-200-1-111000000000000
χ4122-2-222-2-2222-2-2-2-2222-2-2-2-2222222-2-2-2-2222-2-2-2-2-2-2222-2-2-2-222-2-2222200002-2-2222-2-20000000000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ4222-2-222-2-2222-2-2-2-2222-2-2-2-2222222-2-2-2-2222-2-2-2-2-2-2222-2-2-2-222-2-2222200002-2-2222-2-2000000000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ4322-2-2-2-222222-2-2-2-2222-2-222-2-2-2-2-2-22222222-2-2-2-2-2-22222222-2-222-2-2-2-200002-2-22-2-2220000000000000000000000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ4422-2-2-2-222222-2-2-2-2222-2-222-2-2-2-2-2-22222222-2-2-2-2-2-22222222-2-222-2-2-2-200002-2-22-2-222000000000000000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ452-22-22i−2i2i−2i2222-22-2-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i−2i2i−2i00000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ462-22-22i−2i2i−2i2222-22-2-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i−2i2i−2i0000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ472-22-22i−2i2i−2i22-12-2-11-2-212-22i−2i2i−2i−ii2i−2i2i−2i−ii2-1-12-2-11-11-2112i−2i−ii−ii−ii2i−2i−ii0000-1-111−ii−ii0000−i3i3−i3−i3i3i300003−333−3−30000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
χ482-22-22i−2i2i−2i22-12-2-11-2-212-22i−2i2i−2i−ii2i−2i2i−2i−ii2-1-12-2-11-11-2112i−2i−ii−ii−ii2i−2i−ii0000-1-111−ii−ii0000−i3i3−i3−i3i3i300003−333−3−30000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000
χ492-22-22i−2i2i−2i22-12-2-11-2-212-22i−2i2i−2i−ii2i−2i2i−2i−ii2-1-12-2-11-11-2112i−2i−ii−ii−ii2i−2i−ii0000-1-111−ii−ii0000i3−i3i3i3−i3−i30000−33−3−3330000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000
χ502-22-22i−2i2i−2i22-12-2-11-2-212-22i−2i2i−2i−ii2i−2i2i−2i−ii2-1-12-2-11-11-2112i−2i−ii−ii−ii2i−2i−ii0000-1-111−ii−ii0000i3−i3i3i3−i3−i30000−33−3−3330000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
χ512-22-2−2i2i−2i2i2222-22-2-2-2-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2222-22-22-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000022-2-2−2i2i−2i2i0000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.