Finite Group Databasebeta

← Group #72227227

Character table — Group #72227227

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size111111112222222244444444444444444444444444444444444444444444448888888888888888888888888888888888888832323232323232323232323232323232323232323232323232323232323232326464646464646464
order1222222244444444444444444488888888888888888888888888888888888888888816161616161616161616161616161616161616161616161616161616161616168888888816161616161616161616161616161616161616161616161622224444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ711111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ91111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1
χ101111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111
χ111111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111
χ121111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1
χ131111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ141111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ151111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ171111-1-1-1-11111-1-1-1-1ii−i−i1-1ii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−ii−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ31-11-1i−ii−i
χ181111-1-1-1-11111-1-1-1-1ii−i−i1-1ii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−ii−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-11-11−ii−ii
χ191111-1-1-1-11111-1-1-1-1ii−i−i1-1ii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−ii−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-11-11−ii−ii
χ201111-1-1-1-11111-1-1-1-1ii−i−i1-1ii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−ii−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ31-11-1i−ii−i
χ211111-1-1-1-11111-1-1-1-1ii−i−i1-1ii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−ii−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1-11i−i−ii
χ221111-1-1-1-11111-1-1-1-1ii−i−i1-1ii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−ii−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-111-1−iii−i
χ231111-1-1-1-11111-1-1-1-1ii−i−i1-1ii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−ii−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-111-1−iii−i
χ241111-1-1-1-11111-1-1-1-1ii−i−i1-1ii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−ii−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ31-1-11i−i−ii
χ251111-1-1-1-11111-1-1-1-1−i−iii1-1−i−iii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-11-1−ii−ii
χ261111-1-1-1-11111-1-1-1-1−i−iii1-1−i−iii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-11-11i−ii−i
χ271111-1-1-1-11111-1-1-1-1−i−iii1-1−i−iii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-11-11i−ii−i
χ281111-1-1-1-11111-1-1-1-1−i−iii1-1−i−iii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-11-1−ii−ii
χ291111-1-1-1-11111-1-1-1-1−i−iii1-1−i−iii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1-11−iii−i
χ301111-1-1-1-11111-1-1-1-1−i−iii1-1−i−iii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-111-1i−i−ii
χ311111-1-1-1-11111-1-1-1-1−i−iii1-1−i−iii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-111-1i−i−ii
χ321111-1-1-1-11111-1-1-1-1−i−iii1-1−i−iii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1-11−iii−i
χ332222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000002-22-22-22-200000000000000000000000000000000
χ342222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000-22-22-22-2200000000000000000000000000000000
χ3522222222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ3622222222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ3722222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ3822222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ392222222222222222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ402222222222222222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ412222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222222222222222-2-2-2-200000000000000000000000000000000000000002-22-2-22-22000000000000000000000000
χ422222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222222222222222-2-2-2-20000000000000000000000000000000000000000-22-222-22-2000000000000000000000000
χ432222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-22222-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ442222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-222222222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ452222222222-2-222-2-22222-2-2-2-2-2-2000000000000000022-2-222-2-20000-2-20000-2-2220000000022-2-2000022-2-2000022-2-2000022-2-20000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ462222222222-2-222-2-22222-2-2-2-2-2-2000000000000000022-2-222-2-20000-2-20000-2-2220000000022-2-2000022-2-2000022-2-2000022-2-20000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ472222222222-2-222-2-22222-2-2-2-2-2-2000000000000000022-2-222-2-20000-2-20000-2-22200000000-2-2220000-2-2220000-2-2220000-2-2220000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ482222222222-2-222-2-22222-2-2-2-2-2-2000000000000000022-2-222-2-20000-2-20000-2-22200000000-2-2220000-2-2220000-2-2220000-2-2220000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ492222222222-2-222-2-2-2-2-2-2-2-22222000000000000000022-2-222-2-2000022000022-2-20000000022-2-2000022-2-20000-2-2220000-2-22200000000000000002−22−2−22−222−22−2−22−2200000000
χ502222222222-2-222-2-2-2-2-2-2-2-22222000000000000000022-2-222-2-2000022000022-2-20000000022-2-2000022-2-20000-2-2220000-2-2220000000000000000−22−222−22−2−22−222−22−200000000
χ512222222222-2-222-2-2-2-2-2-2-2-22222000000000000000022-2-222-2-2000022000022-2-200000000-2-2220000-2-222000022-2-2000022-2-200000000000000002−22−2−22−22−22−222−22−200000000
χ522222222222-2-222-2-2-2-2-2-2-2-22222000000000000000022-2-222-2-2000022000022-2-200000000-2-2220000-2-222000022-2-2000022-2-20000000000000000−22−222−22−22−22−2−22−2200000000
χ532222-2-2-2-22222-2-2-2-22i2i−2i−2i2-22i2i−2i−2i2222-2-2-2-2-2-2-2-22222-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i2i2i−2i2i−2i−2i2i2i000000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ542222-2-2-2-22222-2-2-2-22i2i−2i−2i2-22i2i−2i−2i2222-2-2-2-2-2-2-2-22222-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i2i2i−2i2i−2i−2i2i2i00000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ552222-2-2-2-22222-2-2-2-22i2i−2i−2i2-22i2i−2i−2i-2-2-2-222222222-2-2-2-2-2-2-2-22222−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i−2i2i2i2i−2i−2i00000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.