Finite Group Databasebeta

← Group #99731

Character table — Group #99731

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222222222222222222244444444444444444444444444444444444488888888888888888888888888888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ1711111-1-1-1-1-1111-1-1-11111-1-1-1-1ii−i−iiii−i−i−iiiii−i−i−i−iii−i−ii−i11-1-111-1-1ii−i−iζζζζ−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ31-11-1i−ii−i
χ1811111-1-1-1-1-1111-1-1-11111-1-1-1-1ii−i−iiii−i−i−iiiii−i−i−i−iii−i−ii−i11-1-111-1-1ii−i−iζζζζ−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3-11-11−ii−ii
χ1911111-1-1-1-1-1111-1-1-11111-1-1-1-1ii−i−iiii−i−i−iiiii−i−i−i−iii−i−ii−i11-1-111-1-1ii−i−i−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3-11-11−ii−ii
χ2011111-1-1-1-1-1111-1-1-11111-1-1-1-1ii−i−iiii−i−i−iiiii−i−i−i−iii−i−ii−i11-1-111-1-1ii−i−i−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ31-11-1i−ii−i
χ2111111-1-1-1-1-1111-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−i−i−iiiii−i−iii−ii11-1-111-1-1−i−iiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζ1-11-1−ii−ii
χ2211111-1-1-1-1-1111-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−i−i−iiiii−i−iii−ii11-1-111-1-1−i−iiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ-11-11i−ii−i
χ2311111-1-1-1-1-1111-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−i−i−iiiii−i−iii−ii11-1-111-1-1−i−iii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζζζζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζ-11-11i−ii−i
χ2411111-1-1-1-1-1111-1-1-11111-1-1-1-1−i−iii−i−i−iiii−i−i−i−iiiii−i−iii−ii11-1-111-1-1−i−iii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ1-11-1−ii−ii
χ2511111-1-1-1-1-1111-1-1-1-1-1-1-11111ii−i−iiii−i−i−i−i−i−i−iiiiiii−i−ii−i11-1-1-1-111−i−iiiζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ31-1-11i−i−ii
χ2611111-1-1-1-1-1111-1-1-1-1-1-1-11111ii−i−iiii−i−i−i−i−i−i−iiiiiii−i−ii−i11-1-1-1-111−i−iiiζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3-111-1−iii−i
χ2711111-1-1-1-1-1111-1-1-1-1-1-1-11111ii−i−iiii−i−i−i−i−i−i−iiiiiii−i−ii−i11-1-1-1-111−i−iii−ζ−ζ−ζ−ζζζζζζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3-111-1−iii−i
χ2811111-1-1-1-1-1111-1-1-1-1-1-1-11111ii−i−iiii−i−i−i−i−i−i−iiiiiii−i−ii−i11-1-1-1-111−i−iii−ζ−ζ−ζ−ζζζζζζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ31-1-11i−i−ii
χ2911111-1-1-1-1-1111-1-1-1-1-1-1-11111−i−iii−i−i−iiiiiiii−i−i−i−i−i−iii−ii11-1-1-1-111ii−i−iζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζ1-1-11−iii−i
χ3011111-1-1-1-1-1111-1-1-1-1-1-1-11111−i−iii−i−i−iiiiiiii−i−i−i−i−i−iii−ii11-1-1-1-111ii−i−iζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ-111-1i−i−ii
χ3111111-1-1-1-1-1111-1-1-1-1-1-1-11111−i−iii−i−i−iiiiiiii−i−i−i−i−i−iii−ii11-1-1-1-111ii−i−i−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζζζζζ−ζ−ζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζ-111-1i−i−ii
χ3211111-1-1-1-1-1111-1-1-1-1-1-1-11111−i−iii−i−i−iiiiiiii−i−i−i−i−i−iii−ii11-1-1-1-111ii−i−i−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ1-1-11−iii−i
χ332222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222222222222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ3722222-2-2-2-2-2222-2-2-22222-2-2-2-22i2i−2i−2i−2i−2i−2i2i2i2i−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i−2i2i-2-222-2-2222i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ3822222-2-2-2-2-2222-2-2-22222-2-2-2-2−2i−2i2i2i2i2i2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i−2i-2-222-2-222−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ3922222-2-2-2-2-2222-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i−2i−2i−2i−2i2i2i−2i−2i−2i2i-2-22222-2-2−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ4022222-2-2-2-2-2222-2-2-2-2-2-2-22222−2i−2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i2i−2i-2-22222-2-22i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ412222-2222-2-2-2-2-22-2-222-2-222-2-2222200000000000000-2-2-2-200000000002-22-222−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2000000000000000000000000
χ422222-2222-2-2-2-2-22-2-222-2-222-2-2222200000000000000-2-2-2-200000000002-22-2−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−222000000000000000000000000
χ432222-2222-2-2-2-2-22-2-222-2-222-2-2-2-2-2-20000000000000022220000000000-22-22i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ442222-2222-2-2-2-2-22-2-222-2-222-2-2-2-2-2-20000000000000022220000000000-22-22−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ452222-2222-2-2-2-2-22-2-2-2-222-2-222222200000000000000-2-2-2-20000000000-22-2222−2−222−2−2−2−222−2−22222−2−222−2−2−2−222−2−222000000000000000000000000
χ462222-2222-2-2-2-2-22-2-2-2-222-2-222222200000000000000-2-2-2-20000000000-22-22−2−222−2−22222−2−222−2−2−2−222−2−22222−2−222−2−2000000000000000000000000
χ472222-2222-2-2-2-2-22-2-2-2-222-2-222-2-2-2-200000000000000222200000000002-22-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ482222-2222-2-2-2-2-22-2-2-2-222-2-222-2-2-2-200000000000000222200000000002-22-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ492222-2-2-2-222-2-2-2-22222-2-2-2-2222i2i−2i−2i00000000000000−2i−2i2i2i00000000002i−2i−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000000000000000
χ502222-2-2-2-222-2-2-2-22222-2-2-2-2222i2i−2i−2i00000000000000−2i−2i2i2i00000000002i−2i−2i2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000000000000000
χ512222-2-2-2-222-2-2-2-22222-2-2-2-222−2i−2i2i2i000000000000002i2i−2i−2i0000000000−2i2i2i−2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000000000000000
χ522222-2-2-2-222-2-2-2-22222-2-2-2-222−2i−2i2i2i000000000000002i2i−2i−2i0000000000−2i2i2i−2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000000000000000
χ532222-2-2-2-222-2-2-2-222-2-22222-2-22i2i−2i−2i00000000000000−2i−2i2i2i0000000000−2i2i2i−2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000000000000000
χ542222-2-2-2-222-2-2-2-222-2-22222-2-22i2i−2i−2i00000000000000−2i−2i2i2i0000000000−2i2i2i−2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000000000000000
χ552222-2-2-2-222-2-2-2-222-2-22222-2-2−2i−2i2i2i000000000000002i2i−2i−2i00000000002i−2i−2i2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.