Finite Group Databasebeta

← Group #72225179

Character table — Group #72225179

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152
size11112222222222222222224444444444444444444444444444444444444444444444888888888888888888888888888888888888161616161616161616161616161616161616161616161616161616161616161664646464646464646464646464646464
order1222224444444488888888444444888888888888888888888888161616161616161616161616161616164488888888881616161616161616161616161616161616161616161616163232323232323232323232323232323232323232323232323232323232323232222244441616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1111111-1-1-1-1
χ91111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ101111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−iii−i−iii
χ121111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−iii−i−i
χ131111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ141111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ151111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ171111-1-1111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-111111111-1-1-1-1-1-1-1-11111ii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-11-1i−ii−iζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ181111-1-1111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-111111111-1-1-1-1-1-1-1-11111ii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-11-11−ii−ii−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ191111-1-1111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-111111111-1-1-1-1-1-1-1-11111ii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-11-1i−ii−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ201111-1-1111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-111111111-1-1-1-1-1-1-1-11111ii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-11-11−ii−iiζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ211111-1-1111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1111111111111ii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-1-11i−i−iiζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ221111-1-1111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1111111111111ii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-111-1−iii−i−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ231111-1-1111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1111111111111ii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-1-11i−i−ii−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ241111-1-1111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1111111111111ii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-111-1−iii−iζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ251111-1-1111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-111111111-1-1-1-1-1-1-1-11111−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1-11-1−ii−iiζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ261111-1-1111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-111111111-1-1-1-1-1-1-1-11111−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-11-11i−ii−i−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ271111-1-1111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-111111111-1-1-1-1-1-1-1-11111−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1-11-1−ii−ii−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ281111-1-1111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-111111111-1-1-1-1-1-1-1-11111−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-11-11i−ii−iζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ291111-1-1111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-1-1-1111111111111−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−iiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1-1-11−iii−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ301111-1-1111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-1-1-1111111111111−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−iiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-111-1i−i−ii−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ311111-1-1111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-1-1-1111111111111−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−iiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1-1-11−iii−i−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ321111-1-1111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-1-1-1111111111111−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−iiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-111-1i−i−iiζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ332222222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ342222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ352222222222222222222222-2-2-2-22222222222222222222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ362222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ3722222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-222-2-222-2-2000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3822222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-222-2-222-2-2000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3922222222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022-2-2-2-222-2-222000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4022222222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022-2-2-2-222-2-222000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4122222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000-2-222-2-222-2-22200000000000000000000000022−2−222−2−2−2−222−2−22222−2−222−2−2−2−222−2−2220000000000000000
χ4222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000-2-222-2-222-2-222000000000000000000000000−2−222−2−22222−2−222−2−2−2−222−2−22222−2−222−2−20000000000000000
χ4322222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000-2-22222-2-222-2-200000000000000000000000022−2−222−2−2−2−222−2−222−2−222−2−22222−2−222−2−20000000000000000
χ4422222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000-2-22222-2-222-2-2000000000000000000000000−2−222−2−22222−2−222−2−222−2−222−2−2−2−222−2−2220000000000000000
χ4522222222-2-2-2-2222222-2-2-2-22222-2-2000000000000000022-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022-2-222-2-20000000000000000000000002-22-22-22-22-22-22-22-20000000000000000
χ4622222222-2-2-2-2222222-2-2-2-22222-2-2000000000000000022-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000-22-22-22-22-22-22-22-220000000000000000
χ4722222222-2-2-2-2222222-2-2-2-22222-2-2000000000000000022-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000-2-222-2-222000000002-22-22-22-22-22-22-22-200000000000000000000000000000000
χ4822222222-2-2-2-2222222-2-2-2-22222-2-2000000000000000022-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000-2-222-2-22200000000-22-22-22-22-22-22-22-2200000000000000000000000000000000
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χ1498-8-880000-88000042−42−4242−424242−4200000042−42−424200000000008-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1508-8-880000-88000042−42−4242−424242−42000000−424242−420000000000-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1518-8-880000-880000−424242−4242−42−424200000042−42−42420000000000-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.