Finite Group Databasebeta

← Group #218508

Character table — Group #218508

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444444444444488888888888888884444444488888888888888888888888888888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1111-1-1-11111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1111-1-1-1111-1-1-1-111
χ9111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ10111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ12111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11-1-1-111-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1111-1-111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-1-1111-111-1-1-1-111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1111-1-1-11-1-11111-1-1
χ1711111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i111-11-1-1-1i−ii−ii−ii−i
χ1811111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-11-1111−ii−ii−ii−ii
χ1911111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii11-11-11-1-1−ii−iii−ii−i
χ2011111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-1-11-11-111i−ii−i−ii−ii
χ2111111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-11-1-11-11i−i−iii−i−ii
χ2211111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-111-11-1−iii−i−iii−i
χ2311111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i1-1-111-1-11−iii−ii−i−ii
χ2411111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-111-1-111-1i−i−ii−iii−i
χ2511111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii111-11-1-1-1−ii−ii−ii−ii
χ2611111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-1-11-1111i−ii−ii−ii−i
χ2711111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-11-11-1-1i−ii−i−ii−ii
χ2811111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-1-11-11-111−ii−iii−ii−i
χ2911111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-11-1-11-11−iii−i−iii−i
χ3011111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11-111-11-1i−i−iii−i−ii
χ3111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii1-1-111-1-11i−i−ii−iii−i
χ3211111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-111-1-111-1−iii−ii−i−ii
χ332222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i22-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-22222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i22-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ41222-2-2-2-2222-2-2-2-2220000000022-2-222-2-2000000002-22-2000000002-22-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ42222-2-2-2-2222-2-2-2-2220000000022-2-222-2-2000000002-22-2000000002-22-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ43222-2-2-2-2222-2-2-2-2220000000022-2-222-2-200000000-22-2200000000-22-22i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ44222-2-2-2-2222-2-2-2-2220000000022-2-222-2-200000000-22-2200000000-22-22−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ45222-2-2-2-2222-2-2-2-22200000000-2-222-2-222000000002-22-200000000-22-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ46222-2-2-2-2222-2-2-2-22200000000-2-222-2-222000000002-22-200000000-22-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ47222-2-2-2-2222-2-2-2-22200000000-2-222-2-22200000000-22-22000000002-22-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ48222-2-2-2-2222-2-2-2-22200000000-2-222-2-22200000000-22-22000000002-22-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ49222-2-2-2-22-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i000000002-2-22000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ50222-2-2-2-22-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i000000002-2-22000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−222−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ51222-2-2-2-22-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i00000000-222-200000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−2−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ52222-2-2-2-22-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i00000000-222-200000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−222i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ53222-2-2-2-22-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i000000002-2-2200000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ54222-2-2-2-22-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i000000002-2-2200000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ55222-2-2-2-22-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i00000000-222-2000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ56222-2-2-2-22-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i00000000-222-2000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ5722-222-2-2-22i−2i2i2i−2i−2i2i−2i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000002-22i−2i2ζ−2ζ2ζ3−2ζ30000i2−i2i2−i22−22−21−i−1+i1−i−1+i1+i−1−i1+i−1−ii2−i2i2−i22−22−21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ5822-222-2-2-22i−2i2i2i−2i−2i2i−2i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000002-22i−2i2ζ−2ζ2ζ3−2ζ30000−i2i2−i2i2−22−22−1+i1−i−1+i1−i−1−i1+i−1−i1+i−i2i2−i2i2−22−22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ5922-222-2-2-22i−2i2i2i−2i−2i2i−2i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000-22−2i2i−2ζ2ζ−2ζ32ζ30000i2−i2i2−i22−22−21−i−1+i1−i−1+i1+i−1−i1+i−1−i−i2i2−i2i2−22−22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ6022-222-2-2-22i−2i2i2i−2i−2i2i−2i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000-22−2i2i−2ζ2ζ−2ζ32ζ30000−i2i2−i2i2−22−22−1+i1−i−1+i1−i−1−i1+i−1−i1+ii2−i2i2−i22−22−21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ6122-222-2-2-22i−2i2i2i−2i−2i2i−2i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000002-22i−2i−2ζ2ζ−2ζ32ζ30000i2−i2i2−i22−22−2−1+i1−i−1+i1−i−1−i1+i−1−i1+ii2−i2i2−i22−22−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ6222-222-2-2-22i−2i2i2i−2i−2i2i−2i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000002-22i−2i−2ζ2ζ−2ζ32ζ30000−i2i2−i2i2−22−221−i−1+i1−i−1+i1+i−1−i1+i−1−i−i2i2−i2i2−22−221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ6322-222-2-2-22i−2i2i2i−2i−2i2i−2i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000-22−2i2i2ζ−2ζ2ζ3−2ζ30000i2−i2i2−i22−22−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−i2i2−i2i2−22−221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ6422-222-2-2-22i−2i2i2i−2i−2i2i−2i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000-22−2i2i2ζ−2ζ2ζ3−2ζ30000−i2i2−i2i2−22−221−i−1+i1−i−1+i1+i−1−i1+i−1−ii2−i2i2−i22−22−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ6522-222-2-2-2−2i2i−2i−2i2i2i−2i2i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000002-2−2i2i2ζ3−2ζ32ζ−2ζ0000i2−i2i2−i2−22−221+i−1−i1+i−1−i1−i−1+i1−i−1+ii2−i2i2−i2−22−221+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.