Finite Group Databasebeta

← Group #13143854

Character table — Group #13143854

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164
size11111111111111111111111122222222222244444444444466666666666666666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636
order1222334444666666121212121212121222446666121212128888242424242424242433336666666666661212121212121212121212121212121266666666121212121212121224242424242424242424242424242424242424242424242424242424242424248888888824242424242424242424242424242424244466121212121212
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ9111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-1
χ10111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-11111
χ11111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-11111
χ12111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-1
χ13111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−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−iiiii1-11-111-1-111-1-1
χ14111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−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−i-11-11-1-111-1-111
χ15111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−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−iiiii-11-11-1-111-1-111
χ16111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−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−i1-11-111-1-111-1-1
χ172222222222222222222222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000000000000000
χ18222222222222222222222222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000000000000000
χ19222222222222222222222222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000000000000000000000
χ20222222222222222222222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000000000000000000000
χ21222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111-2-2111111-2-2111111000000000000000000000000000000000000
χ22222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-2111111-2-2111111-2-21111000000000000000000000000000000000000
χ23222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-2111111-2-2111111-2-211000000000000000000000000000000000000
χ24222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-2111111-2-2111111-2-2000000000000000000000000000000000000
χ25222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111-2-211111122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111000000000000000000000000000000000000
χ26222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-111-2-2111111-2-21111-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-21111000000000000000000000000000000000000
χ27222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-11111-2-2111111-2-211-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-211000000000000000000000000000000000000
χ28222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222111111-2-2111111-2-2-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-2000000000000000000000000000000000000
χ29222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222-1-1-122-1-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111-2-2111111-2-2111111-2-211111122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000000000000000
χ30222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-12-1-1-1-122-1-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-111-2-2111111-2-2111111-2-2111111-2-21111-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000000000000000
χ31222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-11111-2-2111111-2-2111111-2-2111111-2-211-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000000000000000000000
χ32222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222111111-2-2111111-2-2111111-2-2111111-2-2-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000000000000000000000
χ33222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2-1-1-122-1-1-1-1-1-12-1-1-1-2-2-2-211111111111122-1-1-1-1-1-1-2-21111112i2i−i−i−i−i−i−i−2i−2iiiiiii2i2i−i−i−i−i−i−i−2i−2iiiiiii000000000000000000000000000000000000
χ34222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i-12-1-1-1-122-1-1-1-1-12-1-11111-2-2-2-211111111-1-122-1-1-1-111-2-21111−i−i2i2i−i−i−i−iii−2i−2iiiii−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000000000000000000000000000
χ35222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i-1-12-1-1-1-1-122-1-1-1-12-111111111-2-2-2-21111-1-1-1-122-1-11111-2-211−i−i−i−i2i2i−i−iiiii−2i−2iii−i−i−i−i2i2i−i−iiiii−2i−2iii000000000000000000000000000000000000
χ36222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i-1-1-12-1-1-1-1-1-122-1-1-12111111111111-2-2-2-2-1-1-1-1-1-122111111-2-2−i−i−i−i−i−i2i2iiiiiii−2i−2i−i−i−i−i−i−i2i2iiiiiii−2i−2i000000000000000000000000000000000000
χ37222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i2-1-1-122-1-1-1-1-1-12-1-1-1-2-2-2-211111111111122-1-1-1-1-1-1-2-2111111−2i−2iiiiiii2i2i−i−i−i−i−i−i−2i−2iiiiiii2i2i−i−i−i−i−i−i000000000000000000000000000000000000
χ38222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i-12-1-1-1-122-1-1-1-1-12-1-11111-2-2-2-211111111-1-122-1-1-1-111-2-21111ii−2i−2iiiii−i−i2i2i−i−i−i−iii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000000000000000000000000000
χ39222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i-1-12-1-1-1-1-122-1-1-1-12-111111111-2-2-2-21111-1-1-1-122-1-11111-2-211iiii−2i−2iii−i−i−i−i2i2i−i−iiiii−2i−2iii−i−i−i−i2i2i−i−i000000000000000000000000000000000000
χ40222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i-1-1-12-1-1-1-1-1-122-1-1-12111111111111-2-2-2-2-1-1-1-1-1-122111111-2-2iiiiii−2i−2i−i−i−i−i−i−i2i2iiiiiii−2i−2i−i−i−i−i−i−i2i2i000000000000000000000000000000000000
χ41222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i2-1-1-122-1-1-1-1-1-12-1-1-1-2-2-2-2111111111111-2-211111122-1-1-1-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii−2i−2iiiiiii2i2i−i−i−i−i−i−i000000000000000000000000000000000000
χ42222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i-12-1-1-1-122-1-1-1-1-12-1-11111-2-2-2-21111111111-2-21111-1-122-1-1-1-1−i−i2i2i−i−i−i−iii−2i−2iiiiiii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000000000000000000000000000
χ43222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i-1-12-1-1-1-1-122-1-1-1-12-111111111-2-2-2-211111111-2-211-1-1-1-122-1-1−i−i−i−i2i2i−i−iiiii−2i−2iiiiiii−2i−2iii−i−i−i−i2i2i−i−i000000000000000000000000000000000000
χ44222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i-1-1-12-1-1-1-1-1-122-1-1-12111111111111-2-2-2-2111111-2-2-1-1-1-1-1-122−i−i−i−i−i−i2i2iiiiiii−2i−2iiiiiii−2i−2i−i−i−i−i−i−i2i2i000000000000000000000000000000000000
χ45222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i2-1-1-122-1-1-1-1-1-12-1-1-1-2-2-2-2111111111111-2-211111122-1-1-1-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i2i2i−i−i−i−i−i−i−2i−2iiiiiii000000000000000000000000000000000000
χ46222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i-12-1-1-1-122-1-1-1-1-12-1-11111-2-2-2-21111111111-2-21111-1-122-1-1-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000000000000000000000000000
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χ1576-6-66−3−3i3−3+3i366-6-63+3i33−3i33+3i33−3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i000000002ζ222ζ14−2ζ22−2ζ142ζ222ζ14−2ζ22−2ζ14000000000000
χ1586-6-66−3−3i3−3+3i366-6-63+3i33−3i33+3i33−3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i00000000−2ζ22−2ζ142ζ222ζ14−2ζ22−2ζ142ζ222ζ14000000000000
χ1596-6-66−3−3i3−3+3i3-6-6663+3i33−3i33+3i33−3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i3−3−3i3−3+3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002-2-2200000000−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3000000000000
χ1606-6-66−3−3i3−3+3i3-6-6663+3i33−3i33+3i33−3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i3−3−3i3−3+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-222-2000000001+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i3000000000000
χ1616-6-66−3+3i3−3−3i366-6-63−3i33+3i33−3i33+3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i000000002ζ142ζ22−2ζ14−2ζ222ζ142ζ22−2ζ14−2ζ22000000000000
χ1626-6-66−3+3i3−3−3i366-6-63−3i33+3i33−3i33+3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i00000000−2ζ14−2ζ222ζ142ζ22−2ζ14−2ζ222ζ142ζ22000000000000
χ1636-6-66−3+3i3−3−3i3-6-6663−3i33+3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i3−3+3i3−3−3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002-2-2200000000−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3000000000000
χ1646-6-66−3+3i3−3−3i3-6-6663−3i33+3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i3−3+3i3−3−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-222-2000000001−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.