Finite Group Databasebeta

← Group #13161806

Character table — Group #13161806

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444363636363636363636363636363636363636363636363636363636363636363636363636
order124422233344466666666612121212121212121212121233333666666666666666666666666666666666666666661212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121222446666888888881212121224242424242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111-1-11111-1-1-1-1-1-11111111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111-1-11111-1-1-1-1-1-11111111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111-1-11111-1-1-1-1-1-11111111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii
χ811111-1-11111-1-1-1-1-1-11111111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i
χ911-1-1111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1i−ii−ii−ii−i-1-111ii−i−iii−i−iii−i−iii−i−i
χ1011-1-1111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1−ii−ii−ii−ii-1-111−i−iii−i−iii−i−iii−i−iii
χ1111-1-1111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111i−ii−i−ii−ii11-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211-1-1111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111−ii−iii−ii−i11-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311-1-11-1-1111-111-1-1-1-111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-111111-1-111-1-11-1-1-1-111-1-1-1-11111-1-1-1-111
χ1411-1-11-1-1111-111-1-1-1-111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-11111-111-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511-1-11-1-1111-111-1-1-1-111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1-1-11-1-11-111-1111111-1-1-1-111-1-11111-1-1
χ1611-1-11-1-1111-111-1-1-1-111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-111-11-1-111111-1-11111-1-111-1-1-1-111
χ17222222222-12222222-1-122-12222-1-1-1-122222-1-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100000000-1-1-1-10000000000000000
χ18222222222-12222222-1-122-12222-1-1-1-122222-1-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000000011110000000000000000
χ1922222222-1222222-1-1222-1222-1-1222222-1-1-12-1-1-12-12-122-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-12-12-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000002222000000000000-1-1-1-1-1-1-1-1
χ2022222222-1222222-1-1222-1222-1-1222222-1-1-12-1-1-12-12-122-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-12-12-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-200000000000011111111
χ212222222-122222-1-12222-122-1-1222222-1-122-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-1-12-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000222200000000-1-1-1-1-1-1-1-100000000
χ222222222-122222-1-12222-122-1-1222222-1-122-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-1-12-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-2000000001111111100000000
χ2322222-2-222-12-2-2-2-2-2-2-1-122-12222-1-1-1-1-2-2-2-22-1-1-1-122-2-21122-1-1-1-1-1-1-1-1-2-2-2-211111111111111112-1-1-1-122-2-2112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111111112-22-2-1-11100000000-1-1110000000000000000
χ2422222-2-222-12-2-2-2-2-2-2-1-122-12222-1-1-1-1-2-2-2-22-1-1-1-122-2-21122-1-1-1-1-1-1-1-1-2-2-2-211111111111111112-1-1-1-122-2-2112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-22-2211-1-10000000011-1-10000000000000000
χ2522222-2-22-122-2-2-2-211222-1222-1-12222-2-211-12-1-1-12-1-21-2-2-1-122-1-1-1-1-1-11111-2-2-2-2111111111111-12-1-1-12-1-21-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111110000000000002i2i−2i−2i000000000000−i−i−i−iiiii
χ2622222-2-22-122-2-2-2-211222-1222-1-12222-2-211-12-1-1-12-1-21-2-2-1-122-1-1-1-1-1-11111-2-2-2-2111111111111-12-1-1-12-1-21-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-2111111111111000000000000−2i−2i2i2i000000000000iiii−i−i−i−i
χ2722222-2-2-1222-2-211-2-222-122-1-122222211-2-2-1-12-1-1-121-2-2-2-1-1-1-122-1-1-1-111111111-2-2-2-211111111-1-12-1-1-121-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-211111111000000002i2i−2i−2i00000000−i−i−i−iiiii00000000
χ2822222-2-2-1222-2-211-2-222-122-1-122222211-2-2-1-12-1-1-121-2-2-2-1-1-1-122-1-1-1-111111111-2-2-2-211111111-1-12-1-1-121-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-21111111100000000−2i−2i2i2i00000000iiii−i−i−i−i00000000
χ292222-22-2222-22-222-2-2-2-2222222222-2-222-2-222222-2-2-222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-22222-2-2-2-222222-2-2-222-222-2-222-2-222-2-22222-2-2-2-222-2-222-2-222-2-22222-2-2-2-2000000000000000000000000000000000000
χ302222-22-222-1-22-222-2-21122-12222-1-11122-2-22-1-1-1-1-2-2-22-11-2-21111111122-2-2-1-111-1-111-1-1-1-111112-1-1-1-1-2-2-22-1122-2-2-1-111-1-111-1-1-1-1111122-2-2-1-111-1-111-1-1-1-111110000−i3i3−i3i300000000−i3i3−i3i30000000000000000
χ312222-22-222-1-22-222-2-21122-12222-1-11122-2-22-1-1-1-1-2-2-22-11-2-21111111122-2-2-1-111-1-111-1-1-1-111112-1-1-1-1-2-2-22-1122-2-2-1-111-1-111-1-1-1-1111122-2-2-1-111-1-111-1-1-1-111110000i3−i3i3−i300000000i3−i3i3−i30000000000000000
χ322222-22-22-12-22-22211-2-22-1222-1-122-2-22211-12-1-1-1-21-2-12-211-2-2111111-1-11122-2-2-1-111-1-1-1-11111-12-1-1-1-21-2-12-2-1-11122-2-2-1-111-1-1-1-11111-1-11122-2-2-1-111-1-1-1-1111100000000000000000000000000003−33−33−33−3
χ332222-22-22-12-22-22211-2-22-1222-1-122-2-22211-12-1-1-1-21-2-12-211-2-2111111-1-11122-2-2-1-111-1-1-1-11111-12-1-1-1-21-2-12-2-1-11122-2-2-1-111-1-1-1-11111-1-11122-2-2-1-111-1-1-1-111110000000000000000000000000000−33−33−33−33
χ342222-22-2-122-22-2-1-1-2-2-2-2-122-1-12222-2-2-1-1-2-2-1-12-1-11-2122-21111-2-21111-1-111-1-11122-2-2-1-1-1-11111-1-12-1-11-2122-2-1-111-1-11122-2-2-1-1-1-11111-1-111-1-11122-2-2-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ352222-22-2-122-22-2-1-1-2-2-2-2-122-1-12222-2-2-1-1-2-2-1-12-1-11-2122-21111-2-21111-1-111-1-11122-2-2-1-1-1-11111-1-12-1-11-2122-2-1-111-1-11122-2-2-1-1-1-11111-1-111-1-11122-2-2-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ362222-2-22222-2-22-2-222-2-2222222222-2-2-2-22222222-2-22-2-22-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-2-2-2222222222-2-22-2-2222-2-222-2-222-2-22222-2-2-2-2-2-222-2-222-2-222-2-2-2-22222000000000000000000000000000000000000
χ372222-2-2222-1-2-22-2-2221122-12222-1-111-2-2222-1-1-1-1-2-22-21-1-2-211111111-2-22211-1-111-1-11111-1-1-1-12-1-1-1-1-2-22-21-122-2-2-1-111-1-111-1-1-1-11111-2-22211-1-111-1-11111-1-1-1-10000−i3i3i3−i300000000−i3i3i3−i30000000000000000
χ382222-2-2222-1-2-22-2-2221122-12222-1-111-2-2222-1-1-1-1-2-22-21-1-2-211111111-2-22211-1-111-1-11111-1-1-1-12-1-1-1-1-2-22-21-122-2-2-1-111-1-111-1-1-1-11111-2-22211-1-111-1-11111-1-1-1-10000i3−i3−i3i300000000i3−i3−i3i30000000000000000
χ392222-2-222-12-2-22-2-2-1-1-2-22-1222-1-122-2-2-2-2-1-1-12-1-1-1-2121-2211-2-211111111-1-1-2-22211-1-11111-1-1-1-1-12-1-1-1-2121-22-1-11122-2-2-1-111-1-1-1-1111111-1-1-2-22211-1-11111-1-1-1-10000000000000000000000000000−i3i3−i3i3i3−i3i3−i3
χ402222-2-222-12-2-22-2-2-1-1-2-22-1222-1-122-2-2-2-2-1-1-12-1-1-1-2121-2211-2-211111111-1-1-2-22211-1-11111-1-1-1-1-12-1-1-1-2121-22-1-11122-2-2-1-111-1-1-1-1111111-1-1-2-22211-1-11111-1-1-1-10000000000000000000000000000i3−i3i3−i3−i3i3−i3i3
χ412222-2-22-122-2-221122-2-2-122-1-12222-2-21122-1-12-1-11-2-1-2-221111-2-2111111-1-111-1-1-2-2221111-1-1-1-1-1-12-1-11-2-1-2-22-1-111-1-11122-2-2-1-1-1-1111111-1-111-1-1-2-2221111-1-1-1-1000000000000000000003−33−3−33−3300000000
χ422222-2-22-122-2-221122-2-2-122-1-12222-2-21122-1-12-1-11-2-1-2-221111-2-2111111-1-111-1-1-2-2221111-1-1-1-1-1-12-1-11-2-1-2-22-1-111-1-11122-2-2-1-1-1-1111111-1-111-1-1-2-2221111-1-1-1-100000000000000000000−33−333−33−300000000
χ4322-2-222222-1-2-2-22222-1-122-1-2-2-2-21111-2-2-2-22-1-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2-211-2-2-2-21111111111111111-2-2-2-211111111111111112-2-22-1-1110000000011-1-10000000000000000
χ4422-2-222222-1-2-2-22222-1-122-1-2-2-2-21111-2-2-2-22-1-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2-211-2-2-2-21111111111111111-2-2-2-21111111111111111-222-211-1-100000000-1-1110000000000000000
χ4522-2-22222-12-2-2-222-1-1222-12-2-211-2-2-2-2-2-211-12-1-1-12-12-122-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-21-21-2-21111-2-2-2-21111111111111111-2-2-2-21111111111110000000000002i−2i2i−2i000000000000−i−iii−i−iii
χ4622-2-22222-12-2-2-222-1-1222-12-2-211-2-2-2-2-2-211-12-1-1-12-12-122-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-21-21-2-21111-2-2-2-21111111111111111-2-2-2-2111111111111000000000000−2i2i−2i2i000000000000ii−i−iii−i−i
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.