Finite Group Databasebeta

← Group #13144388

Character table — Group #13144388

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164
size11111111111111111111111122222222222244444444444466666666666666666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636
order122233444466666612121212121212122244666612121212444412121212121212123333666666666666121212121212121212121212121212126666666612121212121212121212121212121212121212121212121212121212121212121212121212121212888888882424242424242424242424242424242444441212121212121212
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
χ5111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ6111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111
χ7111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ8111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1
χ911-1-11111-1-111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111i−ii−iii−i−iii−i−i11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-11111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i
χ1011-1-11111-1-111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111i−ii−iii−i−iii−i−i11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111-1-1-1-11111-1-1-1-11111−ii−ii−i−iii−i−iii
χ1111-1-11111-1-111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111−ii−ii−i−iii−i−iii11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-11111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii
χ1211-1-11111-1-111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111−ii−ii−i−iii−i−iii11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111-1-1-1-11111-1-1-1-11111i−ii−iii−i−iii−i−i
χ1311-1-111-1-11111-1-1-1-1-1-1-1-11111-11-11-1-111-1-111i−i−iiii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iii
χ1411-1-111-1-11111-1-1-1-1-1-1-1-11111-11-11-1-111-1-111i−i−iiii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1-1-1-1-111111111-1-1-1-1−iii−i−i−iiiii−i−i
χ1511-1-111-1-11111-1-1-1-1-1-1-1-11111-11-11-1-111-1-111−iii−i−i−iiiii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i
χ1611-1-111-1-11111-1-1-1-1-1-1-1-11111-11-11-1-111-1-111−iii−i−i−iiiii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1-1-1-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii
χ172222222222222222222222222222222222222222222222222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000000000000000
χ18222222222222222222222222222222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000000000000000
χ19222222222222222222222222222222222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000000000000000000000
χ20222222222222222222222222222222222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000000000000000000000
χ21222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-2-2111111-2-2111111-2-2111111-2-2111111000000000000000000000000000000000000
χ22222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-111-2-2111111-2-2111111-2-2111111-2-21111000000000000000000000000000000000000
χ23222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1-1-12-11111-2-2111111-2-2111111-2-2111111-2-211000000000000000000000000000000000000
χ24222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12-1-1-12111111-2-2111111-2-2111111-2-2111111-2-2000000000000000000000000000000000000
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
χ26222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000002-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2111-2111-2111-211100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ27222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000002-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2111-2111-2111-211100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i300i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ28222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-11-2111-2111-2111-211−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000000000000000000000000
χ29222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-11-2111-2111-2111-211i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000000000000000000000000000000000
χ30222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-111-2111-2111-2111-21−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000000000000000000000000000000000
χ31222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-111-2111-2111-2111-21i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000000000000000000000000000000000
χ32222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122111-2111-2111-2111-2−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000000000000000000000000000000000
χ33222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122111-2111-2111-2111-2i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000000000000000000000000000000000
χ34222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-20000000000002222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000000000000000
χ35222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-20000000000002-1-1-12-1-1-122-1-1-1-1-1-1-2-2111111-2-21111112-1-1-12-1-1-1-2111-211100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ36222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-20000000000002-1-1-12-1-1-122-1-1-1-1-1-1-2-2111111-2-21111112-1-1-12-1-1-1-2111-211100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i300−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ37222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2000000000000-12-1-1-12-1-1-1-122-1-1-1-111-2-2111111-2-21111-12-1-1-12-1-11-2111-211−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000000000000000000000000000000000
χ38222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2000000000000-12-1-1-12-1-1-1-122-1-1-1-111-2-2111111-2-21111-12-1-1-12-1-11-2111-211i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000000000000000000000000
χ39222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2000000000000-1-12-1-1-12-1-1-1-1-122-1-11111-2-2111111-2-211-1-12-1-1-12-111-2111-21−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000000000000000000000000000000000
χ40222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2000000000000-1-12-1-1-12-1-1-1-1-122-1-11111-2-2111111-2-211-1-12-1-1-12-111-2111-21i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000000000000000000000000000000000
χ41222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2000000000000-1-1-12-1-1-12-1-1-1-1-1-122111111-2-2111111-2-2-1-1-12-1-1-12111-2111-2−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000000000000000000000000000000000
χ42222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2000000000000-1-1-12-1-1-12-1-1-1-1-1-122111111-2-2111111-2-2-1-1-12-1-1-12111-2111-2i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000000000000000000000000000000000
χ43222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-22222-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111-2111-21112-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111000000000000000000000000000000000000
χ44222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-22222-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-111-2-2111111-2-211111-2111-211-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-21111000000000000000000000000000000000000
χ45222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-22222-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-11111-2-2111111-2-21111-2111-21-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-211000000000000000000000000000000000000
χ46222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-22222-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122111111-2-2111111-2-2111-2111-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-2000000000000000000000000000000000000
χ47222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-222-2-2-2-222222-1-1-12-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111-2111-21112-1-1-12-1-1-1-2-2111111-2-211111122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.