Finite Group Databasebeta

← Group #13137214

Character table — Group #13137214

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204
size111111112222222222222222222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444466666666121212121212121212121212121212121212121212121212121212121212121218181818181818182727272727272727363636363636363654545454
order1222444433444466666699912121212121212121818181818181818183636363636363636363636363666999121212121212121212121212121212121212121218181818181818181836363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363622224444666612121212181818181818181818181818363636363636363636363636888888888888888824242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-1111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111-1-1-1-1111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111-1-1-1-1111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111-1-1-1-1111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ91111-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii−i−iii−i−iii
χ111111-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−iii−i−i−i−i−i−iiiiiii−i−iii−i−i−i−iii
χ121111-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iii−i−iiiiiii−i−i−i−i−i−iii−i−iiiii−i−i
χ131111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111ii−i−i−i−iiiiiii−i−i−i−iii−i−i−i−iii−i−iii
χ141111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−iiiii−i−i−i−i−i−iiiii−i−iiiii−i−iii−i−i
χ151111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1ii−i−i−i−iii−i−i−i−iiiiiii−i−i−i−iiiii−i−i
χ161111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−iiiii−i−iiiii−i−i−i−i−i−iiiii−i−i−i−iii
χ1711-1-1i−ii−i111-1i−i1-1-11-1-1111i−iii−i−ii−i111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-111111-1-1ii−i−iii−i−i11-1-1ii−i−i111-1-1-1-1-1-1111-1-1-1iii−i−i−iiiiiii−i−i−i−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-11-1i−ii−i1-11-1i−ii−i111-1-1-1111-1-1-1iii−i−i−iiii−i−i−iζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69ζ21+ζ69−ζ21−ζ69−ζ21−ζ69−ζ15−ζ39−ζ15−ζ39ζ15+ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39
χ1811-1-1i−ii−i111-1i−i1-1-11-1-1111i−iii−i−ii−i111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-111111-1-1ii−i−iii−i−i11-1-1ii−i−i111-1-1-1-1-1-1111-1-1-1iii−i−i−iiiiiii−i−i−i−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-11-1i−ii−i1-11-1i−ii−i111-1-1-1111-1-1-1iii−i−i−iiii−i−i−i−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69−ζ21−ζ69ζ21+ζ69ζ21+ζ69ζ15+ζ39ζ15+ζ39−ζ15−ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39
χ1911-1-1i−ii−i111-1i−i1-1-11-1-1111i−iii−i−ii−i111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-111111-1-1ii−i−iii−i−i11-1-1ii−i−i111-1-1-1-1-1-1111-1-1-1iii−i−i−iiiiiii−i−i−i−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11-11−ii−ii-11-11−ii−ii-1-1-1111-1-1-1111−i−i−iiii−i−i−iiiiζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39−ζ21−ζ69−ζ21−ζ69ζ21+ζ69ζ21+ζ69ζ15+ζ39ζ15+ζ39−ζ15−ζ39−ζ15−ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39
χ2011-1-1i−ii−i111-1i−i1-1-11-1-1111i−iii−i−ii−i111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-111111-1-1ii−i−iii−i−i11-1-1ii−i−i111-1-1-1-1-1-1111-1-1-1iii−i−i−iiiiiii−i−i−i−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11-11−ii−ii-11-11−ii−ii-1-1-1111-1-1-1111−i−i−iiii−i−i−iiii−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39ζ21+ζ69ζ21+ζ69−ζ21−ζ69−ζ21−ζ69−ζ15−ζ39−ζ15−ζ39ζ15+ζ39ζ15+ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39
χ2111-1-1i−ii−i11-11−ii1-1-11-1-1111i−iii−i−ii−i111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1111-1-111−i−iiiii−i−i-1-111−i−iii111-1-1-1-1-1-1-1-1-1111−i−i−iiiiiiiiii−i−i−i−i−i−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii1-1-11i−i−ii1-1-11i−i−ii111-1-1-1-1-1-1111iii−i−i−i−i−i−iiiiζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39ζ21+ζ69ζ21+ζ69−ζ21−ζ69−ζ21−ζ69−ζ15−ζ39−ζ15−ζ39ζ15+ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39
χ2211-1-1i−ii−i11-11−ii1-1-11-1-1111i−iii−i−ii−i111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1111-1-111−i−iiiii−i−i-1-111−i−iii111-1-1-1-1-1-1-1-1-1111−i−i−iiiiiiiiii−i−i−i−i−i−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii1-1-11i−i−ii1-1-11i−i−ii111-1-1-1-1-1-1111iii−i−i−i−i−i−iiii−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39−ζ21−ζ69−ζ21−ζ69ζ21+ζ69ζ21+ζ69ζ15+ζ39ζ15+ζ39−ζ15−ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39
χ2311-1-1i−ii−i11-11−ii1-1-11-1-1111i−iii−i−ii−i111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1111-1-111−i−iiiii−i−i-1-111−i−iii111-1-1-1-1-1-1-1-1-1111−i−i−iiiiiiiiii−i−i−i−i−i−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii-111-1−iii−i-111-1−iii−i-1-1-1111111-1-1-1−i−i−iiiiiii−i−i−iζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69−ζ21−ζ69ζ21+ζ69ζ21+ζ69ζ15+ζ39ζ15+ζ39−ζ15−ζ39−ζ15−ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39
χ2411-1-1i−ii−i11-11−ii1-1-11-1-1111i−iii−i−ii−i111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1111-1-111−i−iiiii−i−i-1-111−i−iii111-1-1-1-1-1-1-1-1-1111−i−i−iiiiiiiiii−i−i−i−i−i−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii-111-1−iii−i-111-1−iii−i-1-1-1111111-1-1-1−i−i−iiiiiii−i−i−i−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69ζ21+ζ69−ζ21−ζ69−ζ21−ζ69−ζ15−ζ39−ζ15−ζ39ζ15+ζ39ζ15+ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39
χ2511-1-1−ii−ii111-1−ii1-1-11-1-1111−ii−i−iii−ii111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii11-1-111111-1-1−i−iii−i−iii11-1-1−i−iii111-1-1-1-1-1-1111-1-1-1−i−i−iiii−i−i−i−i−i−iiiiiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-11-1−ii−ii1-11-1−ii−ii111-1-1-1111-1-1-1−i−i−iiii−i−i−iiii−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39−ζ15−ζ39ζ15+ζ39ζ15+ζ39ζ21+ζ69ζ21+ζ69−ζ21−ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69
χ2611-1-1−ii−ii111-1−ii1-1-11-1-1111−ii−i−iii−ii111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii11-1-111111-1-1−i−iii−i−iii11-1-1−i−iii111-1-1-1-1-1-1111-1-1-1−i−i−iiii−i−i−i−i−i−iiiiiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-11-1−ii−ii1-11-1−ii−ii111-1-1-1111-1-1-1−i−i−iiii−i−i−iiiiζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39ζ15+ζ39−ζ15−ζ39−ζ15−ζ39−ζ21−ζ69−ζ21−ζ69ζ21+ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69
χ2711-1-1−ii−ii111-1−ii1-1-11-1-1111−ii−i−iii−ii111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii11-1-111111-1-1−i−iii−i−iii11-1-1−i−iii111-1-1-1-1-1-1111-1-1-1−i−i−iiii−i−i−i−i−i−iiiiiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11-11i−ii−i-11-11i−ii−i-1-1-1111-1-1-1111iii−i−i−iiii−i−i−i−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69ζ15+ζ39ζ15+ζ39−ζ15−ζ39−ζ15−ζ39−ζ21−ζ69−ζ21−ζ69ζ21+ζ69ζ21+ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69
χ2811-1-1−ii−ii111-1−ii1-1-11-1-1111−ii−i−iii−ii111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii11-1-111111-1-1−i−iii−i−iii11-1-1−i−iii111-1-1-1-1-1-1111-1-1-1−i−i−iiii−i−i−i−i−i−iiiiiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11-11i−ii−i-11-11i−ii−i-1-1-1111-1-1-1111iii−i−i−iiii−i−i−iζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69−ζ15−ζ39−ζ15−ζ39ζ15+ζ39ζ15+ζ39ζ21+ζ69ζ21+ζ69−ζ21−ζ69−ζ21−ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69
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Here ζ is a primitive root of unity of order 72 (ζ72 = 1); i = ζ18.