Finite Group Databasebeta

← Group #72227278

Character table — Group #72227278

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888888888888888888832323232323232323232323232323232323232323232323232323232323232326464646464646464
order1222222244444444888888884444444444888888888888888888888888888888888816161616161616161616161616161616161616161616161616161616161616168888888816161616161616161616161616161616161616161616161688888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ511111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1
χ911111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−iii−i−i
χ1011111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−iii−i−iii
χ1111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii−i−iii
χ1211111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiii−i−iii−i−i
χ1311111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i−i−iii
χ1411111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−iiiii−i−i
χ1511111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iiiii−i−i
χ1611111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiii-1-1-1-111111111-1-1-1-1iiii−i−i−i−iii−i−i−i−iii
χ171111-1-1-1-11111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1ii−i−iiii−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ii−i−iii−i−i11-1-111-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ181111-1-1-1-11111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1ii−i−iiii−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3−i−iii−i−iii-1-111-1-111ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ191111-1-1-1-11111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1ii−i−iiii−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3ii−i−iii−i−i11-1-111-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ201111-1-1-1-11111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1ii−i−iiii−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−i−iii−i−iii-1-111-1-111−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ211111-1-1-1-11111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1ii−i−iiii−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3ii−i−i−i−iii11-1-1-1-111−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ221111-1-1-1-11111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1ii−i−iiii−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−i−iiiii−i−i-1-11111-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ231111-1-1-1-11111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1ii−i−iiii−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ii−i−i−i−iii11-1-1-1-111ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ241111-1-1-1-11111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1ii−i−iiii−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3−i−iiiii−i−i-1-11111-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ251111-1-1-1-11111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζii−i−iii−i−i-1-111-1-111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ261111-1-1-1-11111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−i−iii−i−iii11-1-111-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ271111-1-1-1-11111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζii−i−iii−i−i-1-111-1-111−ζ3−ζ3ζ3ζ3−ζ−ζζζζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ281111-1-1-1-11111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−i−iii−i−iii11-1-111-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ291111-1-1-1-11111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζii−i−i−i−iii-1-11111-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ301111-1-1-1-11111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−i−iiiii−i−i11-1-1-1-111−ζ3−ζ3ζ3ζ3−ζ−ζζζζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ311111-1-1-1-11111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζii−i−i−i−iii-1-11111-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ321111-1-1-1-11111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζ−i−iiiii−i−i11-1-1-1-111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ3322222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-222-2-2-2-2-2000000000000000000000000000000002-22-22-22-200000000000000000000000000000000
χ3422222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-222-2-2-2-2-200000000000000000000000000000000-22-22-22-2200000000000000000000000000000000
χ3522222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22-2-222222000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ3622222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22-2-22222200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ372222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ382222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ392222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-22-2-22-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ402222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-22-2-22-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ412222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2000000000000000000000000000000000000000000000000000000002-22-2-22-2200000000
χ422222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000000000000000000000000000-22-222-22-200000000
χ432222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222-222-222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ442222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222-222-22222-2-2-2-22222-2-2-2-222222222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ452222222222-2-222-2-200000000-2-22222-2-2-2-200000000000022-2-222-2-2222200-200-20000000022-2-2000022-2-2000022-2-2000022-2-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ462222222222-2-222-2-200000000-2-22222-2-2-2-200000000000022-2-222-2-2222200-200-20000000022-2-2000022-2-2000022-2-2000022-2-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ472222222222-2-222-2-200000000-2-22222-2-2-2-200000000000022-2-222-2-2222200-200-200000000-2-2220000-2-2220000-2-2220000-2-22200000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ482222222222-2-222-2-200000000-2-22222-2-2-2-200000000000022-2-222-2-2222200-200-200000000-2-2220000-2-2220000-2-2220000-2-22200000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ492222222222-2-222-2-200000000-2-2-2-2-2-2222200000000000022-2-222-2-2-2-2-2-20020020000000022-2-2000022-2-20000-2-2220000-2-22200000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ502222222222-2-222-2-200000000-2-2-2-2-2-2222200000000000022-2-222-2-2-2-2-2-20020020000000022-2-2000022-2-20000-2-2220000-2-22200000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ512222222222-2-222-2-200000000-2-2-2-2-2-2222200000000000022-2-222-2-2-2-2-2-200200200000000-2-2220000-2-222000022-2-2000022-2-200000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ522222222222-2-222-2-200000000-2-2-2-2-2-2222200000000000022-2-222-2-2-2-2-2-200200200000000-2-2220000-2-222000022-2-2000022-2-200000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ532222-2-2-2-22222-2-2-2-222-2-2-2-2222-22i2i−2i−2i2i2i−2i−2i22-2-2-2-2-2-22222-2-2-2-22222−2i−2i2i2i2i2i−2i−2i−2i2i−2i−2i2i2i000000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ542222-2-2-2-22222-2-2-2-222-2-2-2-2222-22i2i−2i−2i2i2i−2i−2i22-2-2-2-2-2-22222-2-2-2-22222−2i−2i2i2i2i2i−2i−2i−2i2i−2i−2i2i2i00000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ552222-2-2-2-22222-2-2-2-222-2-2-2-2222-2−2i−2i2i2i−2i−2i2i2i22-2-2-2-2-2-22222-2-2-2-222222i2i−2i−2i−2i−2i2i2i2i−2i2i2i−2i−2i000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ562222-2-2-2-22222-2-2-2-222-2-2-2-2222-2−2i−2i2i2i−2i−2i2i2i22-2-2-2-2-2-22222-2-2-2-222222i2i−2i−2i−2i−2i2i2i2i−2i2i2i−2i−2i00000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
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χ1348-8-888-8-88008-8008-80000000000000000000000−4i24i24i2−4i2−4i24i24i2−4i20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1358-8-888-8-8800-8800-88888-8-88-8-800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1368-8-888-8-8800-8800-88-8-8-888-88800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1378-8-88-888-8008-800-8800000000000000000000004i2−4i2−4i24i2−4i24i24i2−4i20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1388-8-88-888-8008-800-880000000000000000000000−4i24i24i2−4i24i2−4i2−4i24i20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1398-8-88-888-800-88008-888-888-8-8-800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1408-8-88-888-800-88008-8-8-88-8-888800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.