Finite Group Databasebeta

← Group #13161829

Character table — Group #13161829

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444363636363636363636363636363636363636363636363636363636363636363636363636
order12222233344446666666666666121212121212121233333666666666666666666666666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212444444448888121212121212121212121212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111-1-11111-1-11111-1-1-1-111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111-1-11111-1-11111-1-1-1-111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111-1-11111-1-11111-1-1-1-111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111-1-11111-1-11111-1-1-1-111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911-1-11-1111-11-11-1-1-111-1-1111-1-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1i−ii−ii−ii−i1-11-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1011-1-11-1111-11-11-1-1-111-1-1111-1-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1i−ii−i−ii−ii-11-11ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ1111-1-11-1111-11-11-1-1-111-1-1111-1-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−ii−iii−ii−i-11-11−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ1211-1-11-1111-11-11-1-1-111-1-1111-1-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−ii−ii−ii−ii1-11-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ1311-1-1-11111-1-111-1-1-1-1-111111-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111i−i−iii−i−ii1-1-11ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ1411-1-1-11111-1-111-1-1-1-1-111111-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111i−i−ii−iii−i-111-1ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ1511-1-1-11111-1-111-1-1-1-1-111111-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−iii−ii−i−ii-111-1−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ1611-1-1-11111-1-111-1-1-1-1-111111-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−iii−i−iii−i1-1-11−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
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
χ1822222222-12222222222222-1-1-1222-1-1-1-1222-1-1-1-12-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-12-1222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222200000000-1-1-1-1-1-1-1-10000000000000000
χ1922222222-12222222222222-1-1-1222-1-1-1-1222-1-1-1-12-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-12-1222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200000000111111110000000000000000
χ2022222222-1-2-2-2-2222222222-1-1-12-2-21111-2-22-1-1-1-12-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-21-21-2-2-2-2-2-211111111-2-211111111-2-211111111-2-211111111000000000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2122222222-1-2-2-2-2222222222-1-1-12-2-21111-2-22-1-1-1-12-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-21-21-2-2-2-2-2-211111111-2-211111111-2-211111111-2-211111111000000000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ222222222-12222222-1-1-1-1-12-1222-122222222-12-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100002222000000000000-1-1-1-1-1-1-1-100000000
χ232222222-12222222-1-1-1-1-12-1222-122222222-12-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-20000000000001111111100000000
χ242222222-12-2-2-2-222-1-1-1-1-12-1222-1-2-2-2-2-2-2-2-2-12-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-11-21-2-21-2111-2-211111111-2-211111111-2-211111111-2-211111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ252222222-12-2-2-2-222-1-1-1-1-12-1222-1-2-2-2-2-2-2-2-2-12-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-11-21-2-21-2111-2-211111111-2-211111111-2-211111111-2-211111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ26222222-1222222-1-122222-122222-1-12222-1-1-1-12-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-12222-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ27222222-1222222-1-122222-122222-1-12222-1-1-1-12-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-12222-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000-2-2-2-2000000000000000011111111
χ28222222-122-2-2-2-2-1-122222-12222211-2-2-2-211-1-12-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-2-2-21-21-21111-2-211111111-2-211111111-2-211111111-2-2111100000000000000000000000000003−33−33−33−3
χ29222222-122-2-2-2-2-1-122222-12222211-2-2-2-211-1-12-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-2-2-21-21-21111-2-211111111-2-211111111-2-211111111-2-211110000000000000000000000000000−33−33−33−33
χ302222-2-2222-222-2222-2-2-2-2222222-2-22222-2-222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222000000000000000000000000000000000000
χ312222-2-222-12-2-22222-2-2-2-222-1-1-12221111222-1-1-1-1-21-2122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-12-12-1-2-2-2-222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211111111-2-21111111122-2-200000000-1-1-1-111110000000000000000
χ322222-2-222-12-2-22222-2-2-2-222-1-1-12221111222-1-1-1-1-21-2122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-12-12-1-2-2-2-222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211111111-2-211111111-2-222000000001111-1-1-1-10000000000000000
χ332222-2-222-1-222-2222-2-2-2-222-1-1-12-2-2-1-1-1-1-2-22-1-1-1-1-21-2122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-1-21-212222-2-211111111-2-21111111122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ342222-2-222-1-222-2222-2-2-2-222-1-1-12-2-2-1-1-1-1-2-22-1-1-1-1-21-2122-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-1-1-1-1-21-212222-2-211111111-2-21111111122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ352222-2-22-122-2-2222-111112-1222-122-2-2-2-222-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-1-12-12-21-21-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-211111111-2-2111111000022-2-2000000000000-1-1-1-1111100000000
χ362222-2-22-122-2-2222-111112-1222-122-2-2-2-222-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-1-12-12-21-21-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-111-2-211111111-2-21111110000-2-2220000000000001111-1-1-1-100000000
χ372222-2-22-12-222-222-111112-1222-1-2-22222-2-2-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-11-21-22-12-111-2-211111111-2-2111111-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ382222-2-22-12-222-222-111112-1222-1-2-22222-2-2-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-12-1-1-11-21-22-12-111-2-211111111-2-2111111-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ392222-2-2-1222-2-22-1-12-2-2-2-2-122222-1-1-2-2-2-2-1-1-1-12-1-11-21-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-122221-21-2-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211111111-2-211110000000022-2-20000000000000000-1-1-1-11111
χ402222-2-2-1222-2-22-1-12-2-2-2-2-122222-1-1-2-2-2-2-1-1-1-12-1-11-21-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-122221-21-2-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-11111-2-211111111-2-2111100000000-2-22200000000000000001111-1-1-1-1
χ412222-2-2-122-222-2-1-12-2-2-2-2-12222211222211-1-12-1-11-21-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1-2-2-2-2-12-121111-2-211111111-2-21111-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000000000000000000000003−33−3−33−33
χ422222-2-2-122-222-2-1-12-2-2-2-2-12222211222211-1-12-1-11-21-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-1-12-1-1-2-2-2-2-12-121111-2-211111111-2-21111-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000000000000000000000000−33−333−33−3
χ4322-2-22-22222-22-2-2-2-222-2-2222-2-2-222-2-222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222222-2-222-2-222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22222222222000000000000000000000000000000000000
χ4422-2-22-222-12-22-2-2-2-222-2-222-111-22211-1-1-2-22-1-1-1-12-1-21-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-1-212-1-2-222-2-21111111122-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-10000000000003−3−333−3−330000000000000000
χ4522-2-22-222-12-22-2-2-2-222-2-222-111-22211-1-1-2-22-1-1-1-12-1-21-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-1-212-1-2-222-2-21111111122-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-1000000000000−333−3−333−30000000000000000
χ4622-2-22-222-1-22-22-2-2-222-2-222-111-2-2-2-1-111222-1-1-1-12-1-21-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-12-1-2122-2-222-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112i−2i2i−2i00000000−i−iii−i−iii0000000000000000
χ4722-2-22-222-1-22-22-2-2-222-2-222-111-2-2-2-1-111222-1-1-1-12-1-21-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112-1-1-1-12-1-2122-2-222-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-1-1-1-1-2-211111111−2i2i−2i2i00000000ii−i−iii−i−i0000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.