Finite Group Databasebeta

← Group #13161811

Character table — Group #13161811

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444363636363636363636363636363636363636363636363636363636363636363636363636
order1222223334444666666666666612121212121212123333366666666666666666666666666666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121222444444666688881212121212121212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ51111-1-11111-1-11111-1-1-1-111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111-1-11111-1-11111-1-1-1-111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111-1-11111-1-11111-1-1-1-111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ81111-1-11111-1-11111-1-1-1-111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ91-11-11-111111-1-1-1-1-111-1-1-1-1111-11111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1i−ii−i11-1-1i−ii−i11-1-1ii−i−iii−i−iii−i−iii−i−i
χ101-11-11-111111-1-1-1-1-111-1-1-1-1111-11111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1−ii−ii11-1-1−ii−ii11-1-1−i−iii−i−iii−i−iii−i−iii
χ111-11-11-111111-1-1-1-1-111-1-1-1-1111-11111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-11i−ii−i-1-111−ii−ii-1-111ii−i−iii−i−i−i−iii−i−iii
χ121-11-11-111111-1-1-1-1-111-1-1-1-1111-11111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-11-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-11−ii−ii-1-111i−ii−i-1-111−i−iii−i−iiiii−i−iii−i−i
χ131-11-1-111111-11-1-1-1-1-1-111-1-1111-111-1-111-1-111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11i−i−ii11-1-1i−i−ii-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141-11-1-111111-11-1-1-1-1-1-111-1-1111-111-1-111-1-111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11−iii−i11-1-1−iii−i-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151-11-1-111111-11-1-1-1-1-1-111-1-1111-111-1-111-1-111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1i−i−ii-1-111−iii−i11-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161-11-1-111111-11-1-1-1-1-1-111-1-1111-111-1-111-1-111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1−iii−i-1-111i−i−ii11-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222-2-2-2-22222222222222-2-2-2-2-2-2-2-222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222-122222222222-1-122-1222-1-1-1-1222-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1222222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000-1-1-1-10000-1-1-1-10000000000000000
χ1922222222-122222222222-1-122-1222-1-1-1-1222-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1222222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200001111000011110000000000000000
χ2022222222-1-2-2-2-22222222-1-122-12-2-21111-2-22-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2-2-2-211-2-211111111-2-211111111-2-211111111-2-21111111100000000−i3i3−i3i30000−i3i3−i3i30000000000000000
χ2122222222-1-2-2-2-22222222-1-122-12-2-21111-2-22-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2-2-2-211-2-211111111-2-211111111-2-211111111-2-21111111100000000i3−i3i3−i30000i3−i3i3−i30000000000000000
χ222222222-12222222-1-1-1-1-1222-12-122222222-12-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-1-12-12-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100002222000000000000-1-1-1-1-1-1-1-100000000
χ232222222-12222222-1-1-1-1-1222-12-122222222-12-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-1-12-12-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-20000000000001111111100000000
χ242222222-12-2-2-2-222-1-1-1-1-1222-12-1-2-2-2-2-2-2-2-2-12-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-111-21-21-2-211-2-211111111-2-211111111-2-211111111-2-211111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ252222222-12-2-2-2-222-1-1-1-1-1222-12-1-2-2-2-2-2-2-2-2-12-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-111-21-21-2-211-2-211111111-2-211111111-2-211111111-2-211111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ26222222-1222222-1-12222222-1222-1-12222-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-122-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000000002222000000000000-1-1-1-1-1-1-1-1
χ27222222-1222222-1-12222222-1222-1-12222-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-122-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1000000000000-2-2-2-200000000000011111111
χ28222222-122-2-2-2-2-1-12222222-122211-2-2-2-211-1-12-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21-21-2-2-21111-2-211111111-2-211111111-2-211111111-2-2111100000000000000000000000000003−33−33−33−3
χ29222222-122-2-2-2-2-1-12222222-122211-2-2-2-211-1-12-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21-21-2-2-21111-2-211111111-2-211111111-2-211111111-2-211110000000000000000000000000000−33−33−33−33
χ302222-2-2222-222-2222-2-2-2-2222222-2-22222-2-222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222000000000000000000000000000000000000
χ312222-2-222-12-2-22222-2-2-2-2-1-122-12221111222-1-1-1-1-2-21122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-122-2-2-2-2-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211111111-2-21111111122-2-20000-1-1-1-1000011110000000000000000
χ322222-2-222-12-2-22222-2-2-2-2-1-122-12221111222-1-1-1-1-2-21122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-122-2-2-2-2-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211111111-2-211111111-2-222000011110000-1-1-1-10000000000000000
χ332222-2-222-1-222-2222-2-2-2-2-1-122-12-2-2-1-1-1-1-2-22-1-1-1-1-2-21122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-1-2-2222211-2-211111111-2-21111111122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000−i3i3−i3i30000i3−i3i3−i30000000000000000
χ342222-2-222-1-222-2222-2-2-2-2-1-122-12-2-2-1-1-1-1-2-22-1-1-1-1-2-21122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-1-2-2222211-2-211111111-2-21111111122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000i3−i3i3−i30000−i3i3−i3i30000000000000000
χ352222-2-22-122-2-2222-11111222-12-122-2-2-2-222-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-1-1-1-21-2122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-211111111-2-2111111000022-2-2000000000000-1-1-1-1111100000000
χ362222-2-22-122-2-2222-11111222-12-122-2-2-2-222-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-1-1-1-21-2122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-211111111-2-21111110000-2-2220000000000001111-1-1-1-100000000
χ372222-2-22-12-222-222-11111222-12-1-2-22222-2-2-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-1112-12-1-2-211-2-211111111-2-2111111-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ382222-2-22-12-222-222-11111222-12-1-2-22222-2-2-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-1112-12-1-2-211-2-211111111-2-2111111-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ392222-2-2-1222-2-22-1-12-2-2-2-222-1222-1-1-2-2-2-2-1-1-1-12-1-111-2-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1221-21-222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211111111-2-2111100000000000022-2-2000000000000-1-1-1-11111
χ402222-2-2-1222-2-22-1-12-2-2-2-222-1222-1-1-2-2-2-2-1-1-1-12-1-111-2-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1221-21-222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211111111-2-21111000000000000-2-2220000000000001111-1-1-1-1
χ412222-2-2-122-222-2-1-12-2-2-2-222-122211222211-1-12-1-111-2-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1-2-2-12-12-2-21111-2-211111111-2-21111-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000000000000000000000003−33−3−33−33
χ422222-2-2-122-222-2-1-12-2-2-2-222-122211222211-1-12-1-111-2-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1-2-2-12-12-2-21111-2-211111111-2-21111-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000000000000000000000000−33−333−33−3
χ432-22-22-2222-2-222-2-2-222-2-2-2-2222-2-2-2-2-22222222222-22-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222222-22-2-222-22-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22222222222000000000000000000000000000000000000
χ442-22-22-222-122-2-2-2-2-222-2-21122-1-222-1-111-2-22-1-1-1-12-2-11-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-12-222-2-2-1122-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-22-20000-1-1110000-1-1110000000000000000
χ452-22-22-222-122-2-2-2-2-222-2-21122-1-222-1-111-2-22-1-1-1-12-2-11-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-12-222-2-2-1122-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-1-2-211111111-22-22000011-1-1000011-1-10000000000000000
χ462-22-22-222-1-2-222-2-2-222-2-21122-1-2-2-211-1-1222-1-1-1-12-2-11-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-1-22-2-2221-1-2-21111111122-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-100000000−i3i3i3−i30000−i3i3i3−i30000000000000000
χ472-22-22-222-1-2-222-2-2-222-2-21122-1-2-2-211-1-1222-1-1-1-12-2-11-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-1-22-2-2221-1-2-21111111122-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-100000000i3−i3−i3i30000i3−i3−i3i30000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.