Finite Group Databasebeta

← Group #137613

Character table — Group #137613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order1222222244444444444444444444888888888888888822448888888816161616161616161616161616161616161616161616161616161616161616164444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i
χ6111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii
χ7111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii11-1-111-1-1−i−i−i−iiiii
χ8111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-111-1-111iiii−i−i−i−i
χ911111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1711-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-1ii−i−iii−i−i1111-1-1-1-1ii−i−i1-11-111-1-1ii−i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1-1i−ii−i1-1ζ−ζζ3−ζ3ζ3−ζ3ζ−ζ
χ1811-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-1ii−i−iii−i−i1111-1-1-1-1ii−i−i1-11-111-1-1ii−i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-11−ii−ii-11−ζζ−ζ3ζ3−ζ3ζ3−ζζ
χ1911-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-1ii−i−iii−i−i1111-1-1-1-1ii−i−i1-11-111-1-1ii−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1-1i−ii−i1-1−ζζ−ζ3ζ3−ζ3ζ3−ζζ
χ2011-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-1ii−i−iii−i−i1111-1-1-1-1ii−i−i1-11-111-1-1ii−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-11−ii−ii-11ζ−ζζ3−ζ3ζ3−ζ3ζ−ζ
χ2111-1-11-11-1ii−i−i−i−iii1-1ii−i−i1-1−i−iii−i−iii-1-1-1-11111−i−iii-11-1111-1-1ii−i−iζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-1−iii−i-11ζ3−ζ3−ζζζ−ζ−ζ3ζ3
χ2211-1-11-11-1ii−i−i−i−iii1-1ii−i−i1-1−i−iii−i−iii-1-1-1-11111−i−iii-11-1111-1-1ii−i−iζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-11i−i−ii1-1−ζ3ζ3ζ−ζ−ζζζ3−ζ3
χ2311-1-11-11-1ii−i−i−i−iii1-1ii−i−i1-1−i−iii−i−iii-1-1-1-11111−i−iii-11-1111-1-1ii−i−i−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-1−iii−i-11−ζ3ζ3ζ−ζ−ζζζ3−ζ3
χ2411-1-11-11-1ii−i−i−i−iii1-1ii−i−i1-1−i−iii−i−iii-1-1-1-11111−i−iii-11-1111-1-1ii−i−i−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-11i−i−ii1-1ζ3−ζ3−ζζζ−ζ−ζ3ζ3
χ2511-1-11-11-1−i−iiiii−i−i1-1−i−iii1-1ii−i−iii−i−i-1-1-1-11111ii−i−i-11-1111-1-1−i−iiiζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζ1-1i−i−ii-11ζ−ζ−ζ3ζ3ζ3−ζ3−ζζ
χ2611-1-11-11-1−i−iiiii−i−i1-1−i−iii1-1ii−i−iii−i−i-1-1-1-11111ii−i−i-11-1111-1-1−i−iiiζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζ-11−iii−i1-1−ζζζ3−ζ3−ζ3ζ3ζ−ζ
χ2711-1-11-11-1−i−iiiii−i−i1-1−i−iii1-1ii−i−iii−i−i-1-1-1-11111ii−i−i-11-1111-1-1−i−iii−ζ−ζ−ζ−ζζζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζ1-1i−i−ii-11−ζζζ3−ζ3−ζ3ζ3ζ−ζ
χ2811-1-11-11-1−i−iiiii−i−i1-1−i−iii1-1ii−i−iii−i−i-1-1-1-11111ii−i−i-11-1111-1-1−i−iii−ζ−ζ−ζ−ζζζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζ-11−iii−i1-1ζ−ζ−ζ3ζ3ζ3−ζ3−ζζ
χ2911-1-11-11-1−i−iii−i−iii1-1−i−iii1-1−i−iii−i−iii1111-1-1-1-1−i−iii1-11-111-1-1−i−iiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-1−ii−ii1-1ζ3−ζ3ζ−ζζ−ζζ3−ζ3
χ3011-1-11-11-1−i−iii−i−iii1-1−i−iii1-1−i−iii−i−iii1111-1-1-1-1−i−iii1-11-111-1-1−i−iiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-11i−ii−i-11−ζ3ζ3−ζζ−ζζ−ζ3ζ3
χ3111-1-11-11-1−i−iii−i−iii1-1−i−iii1-1−i−iii−i−iii1111-1-1-1-1−i−iii1-11-111-1-1−i−iii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-1−ii−ii1-1−ζ3ζ3−ζζ−ζζ−ζ3ζ3
χ3211-1-11-11-1−i−iii−i−iii1-1−i−iii1-1−i−iii−i−iii1111-1-1-1-1−i−iii1-11-111-1-1−i−iii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-11i−ii−i-11ζ3−ζ3ζ−ζζ−ζζ3−ζ3
χ332222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ36222222222222-2-2-2-222222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2220000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−2220000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-22200000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
χ3922222222-2-2-2-2222222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-22222-2-22222-2-2-2-2-2-20000000000000000-2-22200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4122222222-2-2-2-22222-2-22222-2-2-2-2-2-20000000000000000-2-22200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-22222000000000000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-22222-2-22222000000000000000022-2-20000000022−2−222−2−2−2−222−2−222−2−222−2−22222−2−222−2−20000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-22222-2-22222000000000000000022-2-200000000−2−222−2−22222−2−222−2−222−2−222−2−2−2−222−2−2220000000000000000
χ4522-2-22-22-22i2i−2i−2i2i2i−2i−2i2-22i2i−2i−2i2-22i2i−2i−2i−2i−2i2i2i-2-2-2-22222−2i−2i2i2i2-22-2-2-222−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4622-2-22-22-22i2i−2i−2i2i2i−2i−2i-22−2i−2i2i2i-22−2i−2i2i2i00000000000000002-2-22000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000000000000000
χ4722-2-22-22-22i2i−2i−2i2i2i−2i−2i-22−2i−2i2i2i-22−2i−2i2i2i00000000000000002-2-2200000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000000000000000
χ4822-2-22-22-22i2i−2i−2i−2i−2i2i2i2-22i2i−2i−2i2-2−2i−2i2i2i2i2i−2i−2i2222-2-2-2-22i2i−2i−2i-22-22-2-222−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4922-2-22-22-22i2i−2i−2i−2i−2i2i2i-22−2i−2i2i2i-222i2i−2i−2i0000000000000000-222-2000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000000000
χ5022-2-22-22-22i2i−2i−2i−2i−2i2i2i-22−2i−2i2i2i-222i2i−2i−2i0000000000000000-222-200000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000000000
χ5122-2-22-22-2−2i−2i2i2i2i2i−2i−2i2-2−2i−2i2i2i2-22i2i−2i−2i−2i−2i2i2i2222-2-2-2-2−2i−2i2i2i-22-22-2-2222i2i−2i−2i000000000000000000000000000000000000000000000000
χ5222-2-22-22-2−2i−2i2i2i2i2i−2i−2i-222i2i−2i−2i-22−2i−2i2i2i0000000000000000-222-2000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000000000000000
χ5322-2-22-22-2−2i−2i2i2i2i2i−2i−2i-222i2i−2i−2i-22−2i−2i2i2i0000000000000000-222-200000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000000000000000
χ5422-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-2−2i−2i2i2i2-2−2i−2i2i2i2i2i−2i−2i-2-2-2-222222i2i−2i−2i2-22-2-2-2222i2i−2i−2i000000000000000000000000000000000000000000000000
χ5522-2-22-22-2−2i−2i2i2i−2i−2i2i2i-222i2i−2i−2i-222i2i−2i−2i00000000000000002-2-22000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000000000
χ5622-2-22-22-2−2i−2i2i2i−2i−2i2i2i-222i2i−2i−2i-222i2i−2i−2i00000000000000002-2-2200000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000000000
χ572-22-2-222-200002i−2i2i−2i2-20000-222i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i0000000000002-22-21+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000000000
χ582-22-2-222-200002i−2i2i−2i2-20000-222i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i0000000000002-22-2−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.