Finite Group Databasebeta

← Group #13135888

Character table — Group #13135888

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164
size11111111111111111111111122222222222244444444444466666666666666666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636
order122222223366666666666666444412121212121212124444121212121212121233336666666666666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212888888882424242424242424242424242424242444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ5111-1-11-1-1111111-1-1-1-111-1-1-1-11-1-1111-1-1-1-111ii−i−iiiii−i−i−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i
χ6111-1-11-1-1111111-1-1-1-111-1-1-1-11-1-1111-1-1-1-111ii−i−iiiii−i−i−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iii−i−i−i−iiiii
χ7111-1-11-1-1111111-1-1-1-111-1-1-1-11-1-1111-1-1-1-111−i−iii−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii
χ8111-1-11-1-1111111-1-1-1-111-1-1-1-11-1-1111-1-1-1-111−i−iii−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−iiiii−i−i−i−i
χ91-1-11-111-111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-11-11-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i
χ101-1-11-111-111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-11-11-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii
χ111-1-11-111-111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-11-11-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii
χ121-1-11-111-111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-11-11-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i
χ131-1-1-111-1111-1-1-1-1-1-11111-1-1111-11-111-1-111-1-1i−i−iiii−i−i−i−iii1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1
χ141-1-1-111-1111-1-1-1-1-1-11111-1-1111-11-111-1-111-1-1i−i−iiii−i−i−i−iii1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111
χ151-1-1-111-1111-1-1-1-1-1-11111-1-1111-11-111-1-111-1-1−iii−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111
χ161-1-1-111-1111-1-1-1-1-1-11111-1-1111-11-111-1-111-1-1−iii−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1
χ172222222222222222222222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000000000000000
χ18222222222222222222222222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000000000000000
χ19222222222222222222222222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000000000000000000000
χ20222222222222222222222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000000000000000000000
χ21222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-2-2111111-2-2111111-2-2111111-2-2111111000000000000000000000000000000000000
χ22222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-111-2-2111111-2-2111111-2-2111111-2-21111000000000000000000000000000000000000
χ23222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-11111-2-2111111-2-2111111-2-2111111-2-211000000000000000000000000000000000000
χ24222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12111111-2-2111111-2-2111111-2-2111111-2-2000000000000000000000000000000000000
χ25222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000022222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000000000000000
χ26222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000002-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1-2111-2111-2111-211100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ27222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000002-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1-2111-2111-2111-211100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i300i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ28222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-11-2111-2111-2111-211−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000000000000000000000000
χ29222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-11-2111-2111-2111-211i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000000000000000000000000000000000
χ30222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-111-2111-2111-2111-21−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000000000000000000000000000000000
χ31222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-111-2111-2111-2111-21i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000000000000000000000000000000000
χ32222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12111-2111-2111-2111-2−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000000000000000000000000000000000
χ33222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12111-2111-2111-2111-2i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000000000000000000000000000000000
χ34222-2-22-2-2222222-2-2-2-222-2-2-2-22-2-2222-2-2-2-2222i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2-1-1-122-1-1-1-1-1-1-2111-2-21111112-1-1-1-21112-1-1-12-1-1-1-2111-21112i2i−i−i−i−i−i−i2i2i−i−i−i−i−i−i−2i−2iiiiiii−2i−2iiiiiii000000000000000000000000000000000000
χ35222-2-22-2-2222222-2-2-2-222-2-2-2-22-2-2222-2-2-2-2222i2i−2i−2i2i2i2i2i−2i−2i−2i−2i-12-1-1-1-122-1-1-1-11-21111-2-21111-12-1-11-211-12-1-1-12-1-11-2111-211−i−i2i2i−i−i−i−i−i−i2i2i−i−i−i−iii−2i−2iiiiiii−2i−2iiiii000000000000000000000000000000000000
χ36222-2-22-2-2222222-2-2-2-222-2-2-2-22-2-2222-2-2-2-2222i2i−2i−2i2i2i2i2i−2i−2i−2i−2i-1-12-1-1-1-1-122-1-111-211111-2-211-1-12-111-21-1-12-1-1-12-111-2111-21−i−i−i−i2i2i−i−i−i−i−i−i2i2i−i−iiiii−2i−2iiiiiii−2i−2iii000000000000000000000000000000000000
χ37222-2-22-2-2222222-2-2-2-222-2-2-2-22-2-2222-2-2-2-2222i2i−2i−2i2i2i2i2i−2i−2i−2i−2i-1-1-12-1-1-1-1-1-122111-2111111-2-2-1-1-12111-2-1-1-12-1-1-12111-2111-2−i−i−i−i−i−i2i2i−i−i−i−i−i−i2i2iiiiiii−2i−2iiiiiii−2i−2i000000000000000000000000000000000000
χ38222-2-22-2-2222222-2-2-2-222-2-2-2-22-2-2222-2-2-2-222−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i2-1-1-122-1-1-1-1-1-1-2111-2-21111112-1-1-1-21112-1-1-12-1-1-1-2111-2111−2i−2iiiiiii−2i−2iiiiiii2i2i−i−i−i−i−i−i2i2i−i−i−i−i−i−i000000000000000000000000000000000000
χ39222-2-22-2-2222222-2-2-2-222-2-2-2-22-2-2222-2-2-2-222−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i-12-1-1-1-122-1-1-1-11-21111-2-21111-12-1-11-211-12-1-1-12-1-11-2111-211ii−2i−2iiiiiii−2i−2iiiii−i−i2i2i−i−i−i−i−i−i2i2i−i−i−i−i000000000000000000000000000000000000
χ40222-2-22-2-2222222-2-2-2-222-2-2-2-22-2-2222-2-2-2-222−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i-1-12-1-1-1-1-122-1-111-211111-2-211-1-12-111-21-1-12-1-1-12-111-2111-21iiii−2i−2iiiiiii−2i−2iii−i−i−i−i2i2i−i−i−i−i−i−i2i2i−i−i000000000000000000000000000000000000
χ41222-2-22-2-2222222-2-2-2-222-2-2-2-22-2-2222-2-2-2-222−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i-1-1-12-1-1-1-1-1-122111-2111111-2-2-1-1-12111-2-1-1-12-1-1-12111-2111-2iiiiii−2i−2iiiiiii−2i−2i−i−i−i−i−i−i2i2i−i−i−i−i−i−i2i2i000000000000000000000000000000000000
χ42222-2-22-2-2222222-2-2-2-222-2-2-2-2-222-2-2-22222-2-2000000000000222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000000000000000
χ43222-2-22-2-2222222-2-2-2-222-2-2-2-2-222-2-2-22222-2-20000000000002-1-1-122-1-1-1-1-1-1-2111-2-21111112-1-1-1-2111-2111-21112-1-1-12-1-1-1003−33−33−3003−33−33−300−33−33−3300−33−33−33000000000000000000000000000000000000
χ44222-2-22-2-2222222-2-2-2-222-2-2-2-2-222-2-2-22222-2-20000000000002-1-1-122-1-1-1-1-1-1-2111-2-21111112-1-1-1-2111-2111-21112-1-1-12-1-1-100−33−33−3300−33−33−33003−33−33−3003−33−33−3000000000000000000000000000000000000
χ45222-2-22-2-2222222-2-2-2-222-2-2-2-2-222-2-2-22222-2-2000000000000-12-1-1-1-122-1-1-1-11-21111-2-21111-12-1-11-2111-2111-211-12-1-1-12-1-13−3003−3−333−3003−3−33−3300−333−3−3300−333−3000000000000000000000000000000000000
χ46222-2-22-2-2222222-2-2-2-222-2-2-2-2-222-2-2-22222-2-2000000000000-12-1-1-1-122-1-1-1-11-21111-2-21111-12-1-11-2111-2111-211-12-1-1-12-1-1−3300−333−3−3300−333−33−3003−3−333−3003−3−33000000000000000000000000000000000000
χ47222-2-22-2-2222222-2-2-2-222-2-2-2-2-222-2-2-22222-2-2000000000000-1-12-1-1-1-1-122-1-111-211111-2-211-1-12-111-2111-2111-21-1-12-1-1-12-13−3−33003−33−3−33003−3−333−300−33−333−300−33000000000000000000000000000000000000
χ48222-2-22-2-2222222-2-2-2-222-2-2-2-2-222-2-2-22222-2-2000000000000-1-12-1-1-1-1-122-1-111-211111-2-211-1-12-111-2111-2111-21-1-12-1-1-12-1−333−300−33−333−300−333−3−33003−33−3−33003−3000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.