Finite Group Databasebeta

← Group #161492

Character table — Group #161492

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222224444444444444444444444444444224444444444888888888888888888888888888888884444444488888888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii11-1-111-1-1−i−i−i−iiiii
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-111-1-111iiii−i−i−i−i
χ9111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ11111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-111
χ12111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1ii−i−i−i−iii
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−iiiii−i−i
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111ii−i−i−i−iii
χ1711111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ1811111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ1911111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ2011111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-111-11-1-11-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1-11-111-11-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-111-1-11-11-111-11-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-111-11-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11-111-1i−i−iii−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-111-11-1-11−iii−i−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11-111-1−iii−i−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-11-1-11i−i−iii−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-11-111-1-11-111-1
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-111-11-1-111-11-1-11
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-1-11-11-111-11-1-11
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-111-11-11-1-11-111-1
χ332222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-222-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-22222-2-2-2-222-2-2-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-22222222222222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-222-2-22222-2-222000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222222222-2-2-2-22222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ41222-22-2-2-222-2-222-2-20000000022-2-22222-2-200000000-2-22-200002-2000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−20000000000000000
χ42222-22-2-2-222-2-222-2-20000000022-2-22222-2-200000000-2-22-200002-20000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
χ43222-22-2-2-222-2-222-2-200000000-2-222-2-2-2-22200000000222-20000-220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ44222-22-2-2-222-2-222-2-200000000-2-222-2-2-2-22200000000222-20000-220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ45222-22-2-2-222-2-2-2-2220000000022-2-222-2-22200000000-2-2-220000-22000022−2−222−2−2−2−222−2−22222−2−222−2−2−2−222−2−2220000000000000000
χ46222-22-2-2-222-2-2-2-2220000000022-2-222-2-22200000000-2-2-220000-220000−2−222−2−22222−2−222−2−2−2−222−2−22222−2−222−2−20000000000000000
χ47222-22-2-2-222-2-2-2-22200000000-2-222-2-222-2-20000000022-2200002-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ48222-22-2-2-222-2-2-2-22200000000-2-222-2-222-2-20000000022-2200002-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ49222-22-2-2-2-2-22222-2-20000000022-2-2-2-222-2-20000000022-220000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ50222-22-2-2-2-2-22222-2-20000000022-2-2-2-222-2-20000000022-220000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ51222-22-2-2-2-2-22222-2-200000000-2-22222-2-22200000000-2-2-2200002-2000022−2−2−2−22222−2−2−2−222−2−22222−2−2−2−22222−2−20000000000000000
χ52222-22-2-2-2-2-22222-2-200000000-2-22222-2-22200000000-2-2-2200002-20000−2−22222−2−2−2−22222−2−222−2−2−2−22222−2−2−2−2220000000000000000
χ53222-22-2-2-2-2-222-2-2220000000022-2-2-2-2-2-22200000000222-200002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ54222-22-2-2-2-2-222-2-2220000000022-2-2-2-2-2-22200000000222-200002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ55222-22-2-2-2-2-222-2-22200000000-2-2222222-2-200000000-2-22-20000-22000022−2−2−2−222−2−22222−2−2−2−22222−2−222−2−2−2−2220000000000000000
χ56222-22-2-2-2-2-222-2-22200000000-2-2222222-2-200000000-2-22-20000-220000−2−22222−2−222−2−2−2−22222−2−2−2−222−2−22222−2−20000000000000000
χ5722-22-2-2-222-22-2000000002i2i−2i−2i2i−2i2i−2i2i−2i000022-2-200002i−2i00002i−2i00002-21+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
χ5822-22-2-2-222-22-2000000002i2i−2i−2i2i−2i2i−2i2i−2i000022-2-200002i−2i00002i−2i00002-2−1−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
χ5922-22-2-2-222-22-2000000002i2i−2i−2i−2i2i−2i2i−2i2i0000-2-2220000−2i2i00002i−2i0000-221−i−1+i1−i−1+i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000000000
χ6022-22-2-2-222-22-2000000002i2i−2i−2i−2i2i−2i2i−2i2i0000-2-2220000−2i2i00002i−2i0000-22−1+i1−i−1+i1−i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000000000
χ6122-22-2-2-222-22-200000000−2i−2i2i2i2i−2i2i−2i2i−2i0000-2-22200002i−2i0000−2i2i0000-221+i−1−i1+i−1−i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
χ6222-22-2-2-222-22-200000000−2i−2i2i2i2i−2i2i−2i2i−2i0000-2-22200002i−2i0000−2i2i0000-22−1−i1+i−1−i1+i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
χ6322-22-2-2-222-22-200000000−2i−2i2i2i−2i2i−2i2i−2i2i000022-2-20000−2i2i0000−2i2i00002-21−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
χ6422-22-2-2-222-22-200000000−2i−2i2i2i−2i2i−2i2i−2i2i000022-2-20000−2i2i0000−2i2i00002-2−1+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
χ6522-22-2-2-22-22-22000000002i2i−2i−2i2i−2i2i−2i−2i2i000022-2-20000−2i2i0000−2i2i0000-221−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i0000000000000000
χ6622-22-2-2-22-22-22000000002i2i−2i−2i2i−2i2i−2i−2i2i000022-2-20000−2i2i0000−2i2i0000-22−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+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.