Finite Group Databasebeta

← Group #72225239

Character table — Group #72225239

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160
size111122222244444444444444448888888888888888888888888888888888888888888888161616161616161616161616161616161616161632323232323232323232323232323232323232323232323232323232323232323232323232323232646464646464646464646464646464646464646464646464128128128128
order12222244444444444488888888448888888888888888888816161616161616161616161616161616161616161616161622224444444444441616161688888888161616161616161616161616161616161616161616161616161616161616161622224444323232323232323232323232323232328888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ5111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1
χ91111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i
χ101111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii
χ111111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iii
χ121111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i
χ131111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iii
χ141111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i
χ151111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i
χ161111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii
χ1711-1-11-111-1-1ii−i−i11-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1ii−i−iii−i−i11-1-11-1i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ311-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ−ζζ3−ζ3
χ1811-1-11-111-1-1ii−i−i11-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1ii−i−iii−i−i11-1-11-1i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ311-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζζ−ζ3ζ3
χ1911-1-11-111-1-1ii−i−i11-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-111-1-11ii−i−i−i−iii11-1-11-1i−i-11−ii11-1-1ii−i−i-1-111−i−iiiζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-1-111−i−iiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζζ−ζ3ζ3
χ2011-1-11-111-1-1ii−i−i11-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-111-1-11ii−i−i−i−iii11-1-11-1i−i-11−ii11-1-1ii−i−i-1-111−i−iii−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-1-111−i−iii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ−ζζ3−ζ3
χ2111-1-11-111-1-1ii−i−i11-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-111-1-111-1−i−iiiii−i−i11-1-1-11−ii1-1i−i-1-111−i−iii11-1-1ii−i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-1-111−i−iii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζζ−ζ3ζ3
χ2211-1-11-111-1-1ii−i−i11-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-111-1-111-1−i−iiiii−i−i11-1-1-11−ii1-1i−i-1-111−i−iii11-1-1ii−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-1-111−i−iiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ−ζζ3−ζ3
χ2311-1-11-111-1-1ii−i−i11-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−i−iii−i−iii11-1-1-11−ii-11−ii-1-111−i−iii-1-111−i−iiiζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ311-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ−ζζ3−ζ3
χ2411-1-11-111-1-1ii−i−i11-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−i−iii−i−iii11-1-1-11−ii-11−ii-1-111−i−iii-1-111−i−iii−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ311-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζζ−ζ3ζ3
χ2511-1-11-111-1-1−i−iii11-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−i−iii−i−iii11-1-11-1−ii1-1−ii11-1-1−i−iii11-1-1−i−iiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3−ζ3ζ−ζ
χ2611-1-11-111-1-1−i−iii11-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−i−iii−i−iii11-1-11-1−ii1-1−ii11-1-1−i−iii11-1-1−i−iii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3ζ3−ζζ
χ2711-1-11-111-1-1−i−iii11-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-111-1-11−i−iiiii−i−i11-1-11-1−ii-11i−i11-1-1−i−iii-1-111ii−i−iζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-1-111ii−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3ζ3−ζζ
χ2811-1-11-111-1-1−i−iii11-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-111-1-11−i−iiiii−i−i11-1-11-1−ii-11i−i11-1-1−i−iii-1-111ii−i−i−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-1-111ii−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3−ζ3ζ−ζ
χ2911-1-11-111-1-1−i−iii11-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-111-1-111-1ii−i−i−i−iii11-1-1-11i−i1-1−ii-1-111ii−i−i11-1-1−i−iiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-1-111ii−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3ζ3−ζζ
χ3011-1-11-111-1-1−i−iii11-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-111-1-111-1ii−i−i−i−iii11-1-1-11i−i1-1−ii-1-111ii−i−i11-1-1−i−iii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-1-111ii−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3−ζ3ζ−ζ
χ3111-1-11-111-1-1−i−iii11-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11ii−i−iii−i−i11-1-1-11i−i-11i−i-1-111ii−i−i-1-111ii−i−iζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3−ζ3ζ−ζ
χ3211-1-11-111-1-1−i−iii11-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11ii−i−iii−i−i11-1-1-11i−i-11i−i-1-111ii−i−i-1-111ii−i−i−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3ζ3−ζζ
χ33222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-200000000000000000000000000000000000000002-22-22-22-200000000000000000000
χ34222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-20000000000000000000000000000000000000000-22-22-22-2200000000000000000000
χ3522222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-222-2-222-2-200220022000022222-22-20000222200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ3622222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-222-2-222-2-200-2-200-2-20000-2-2-2-22-22-20000-2-2-2-2000000002222222200000000000000000000000000000000000000000000
χ3722222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-222-2-2222200220022220000-22-2222220000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000
χ3822222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-222-2-222-2-200-2-200-2-2-2-20000-22-22-2-2-2-20000222222220000000000000000000000000000000000000000000000000000
χ3922222222222222-2-2-2-22-22-22-22-2-2-22-22-20000000000000000002200220022002200-2-200-2-222002200222200000-20-2-2-2-2-200000000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000i2−i2i2−i2i2−i2i2−i2000000000000
χ4022222222222222-2-2-2-22-22-22-22-2-2-22-22-20000000000000000002200220022002200-2-200-2-222002200222200000-20-2-2-2-2-200000000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000−i2i2−i2i2−i2i2−i2i2000000000000
χ4122222222222222-2-2-2-22-22-22-22-2-2-22-22-20000000000000000002200220022002200-2-200-2-2-2-200-2-200-2-2-2-200000-20-2222200000000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000−i2i2−i2i2−i2i2−i2i2000000000000
χ4222222222222222-2-2-2-22-22-22-22-2-2-22-22-20000000000000000002200220022002200-2-200-2-2-2-200-2-200-2-2-2-200000-20-2222200000000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000i2−i2i2−i2i2−i2i2−i2000000000000
χ4322222222222222-2-2-2-2-22-22-22-22-2-2-22-2200000000000000002200220022002200-2-200-2-2000022002200002222-20-200000-2-2-2-20000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000i2−i2i2−i2i2−i2i2−i20000
χ4422222222222222-2-2-2-2-22-22-22-22-2-2-22-2200000000000000002200220022002200-2-200-2-2000022002200002222-20-200000-2-2-2-20000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000−i2i2−i2i2−i2i2−i2i20000
χ4522222222222222-2-2-2-2-22-22-22-22-2-2-22-2200000000000000002200220022002200-2-200-2-20000-2-200-2-20000-2-2-2-2-20-20000022220000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000−i2i2−i2i2−i2i2−i2i20000
χ4622222222222222-2-2-2-2-22-22-22-22-2-2-22-2200000000000000002200220022002200-2-200-2-20000-2-200-2-20000-2-2-2-2-20-20000022220000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000i2−i2i2−i2i2−i2i2−i20000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.