Finite Group Databasebeta

← Group #210263

Character table — Group #210263

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12224444888888882244444488888888444444444488888888888888888888888888222444444444888888888888888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111111111111111111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-111111111-1-1-1-111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-11111-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11111-1-111
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-111
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-111-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1
χ171111-1-1-1-1iiii−i−i−i−i-1-1111-1-11ii−i−iii−i−i11-1-111-1-11-1i−iii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1111-1-1-11-1ii−i−ii−iii−i−ii−iii−i−i11-1-111-1-11-1i−i
χ181111-1-1-1-1iiii−i−i−i−i-1-1111-1-11ii−i−iii−i−i11-1-111-1-11-1i−iii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111111-1-1-11-1−i−iiii−iii−i−ii−i−i−iii-1-111-1-111-11−ii
χ191111-1-1-1-1iiii−i−i−i−i-1-1111-1-11ii−i−iii−i−i11-1-1-1-1111-1i−iii−i−i−i−iiiiiii−i−i−i−i1111-1-1-1-11-1-1-111-11−i−iiii−i−i−iii−iiii−i−i11-1-1-1-111-11−ii
χ201111-1-1-1-1iiii−i−i−i−i-1-1111-1-11ii−i−iii−i−i11-1-1-1-1111-1i−iii−i−i−i−iii−i−i−i−iiiii-1-1-1-111111-1-1-111-11ii−i−ii−i−i−iii−ii−i−iii-1-11111-1-11-1i−i
χ211111-1-1-1-1iiii−i−i−i−i-1-1111-1-11ii−i−iii−i−i-1-11111-1-11-1i−i−i−iiiii−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-11111-1ii−i−i−ii−i−iiii−i−i−iii-1-11111-1-1-11−ii
χ221111-1-1-1-1iiii−i−i−i−i-1-1111-1-11ii−i−iii−i−i-1-11111-1-11-1i−i−i−iiiii−i−i−i−i−i−iiiii-1-1-1-11111-1-1-11111-1−i−iii−ii−i−iiii−iii−i−i11-1-1-1-1111-1i−i
χ231111-1-1-1-1iiii−i−i−i−i-1-1111-1-11ii−i−iii−i−i-1-111-1-1111-1i−i−i−iii−i−iiiiiii−i−i−i−i1111-1-1-1-1-1111-1-1-11−i−iii−iiii−i−i−ii−i−iii-1-111-1-1111-1i−i
χ241111-1-1-1-1iiii−i−i−i−i-1-1111-1-11ii−i−iii−i−i-1-111-1-1111-1i−i−i−iii−i−iii−i−i−i−iiiii-1-1-1-11111-1111-1-1-11ii−i−i−iiii−i−i−iiii−i−i11-1-111-1-1-11−ii
χ251111-1-1-1-1−i−i−i−iiiii-1-1111-1-11−i−iii−i−iii11-1-111-1-11-1−ii−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111111-1-1-11-1ii−i−i−ii−i−iii−iiii−i−i-1-111-1-111-11i−i
χ261111-1-1-1-1−i−i−i−iiiii-1-1111-1-11−i−iii−i−iii11-1-111-1-11-1−ii−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1111-1-1-11-1−i−iii−ii−i−iii−ii−i−iii11-1-111-1-11-1−ii
χ271111-1-1-1-1−i−i−i−iiiii-1-1111-1-11−i−iii−i−iii11-1-1-1-1111-1−ii−i−iiiii−i−iiiii−i−i−i−i-1-1-1-111111-1-1-111-11−i−iii−iiii−i−ii−iii−i−i-1-11111-1-11-1−ii
χ281111-1-1-1-1−i−i−i−iiiii-1-1111-1-11−i−iii−i−iii11-1-1-1-1111-1−ii−i−iiiii−i−i−i−i−i−iiiii1111-1-1-1-11-1-1-111-11ii−i−i−iiii−i−ii−i−i−iii11-1-1-1-111-11i−i
χ291111-1-1-1-1−i−i−i−iiiii-1-1111-1-11−i−iii−i−iii-1-11111-1-11-1−iiii−i−i−i−iiiiiii−i−i−i−i-1-1-1-11111-1-1-11111-1ii−i−ii−iii−i−i−ii−i−iii11-1-1-1-1111-1−ii
χ301111-1-1-1-1−i−i−i−iiiii-1-1111-1-11−i−iii−i−iii-1-11111-1-11-1−iiii−i−i−i−iii−i−i−i−iiiii1111-1-1-1-1-1-1-11111-1−i−iiii−iii−i−i−iiii−i−i-1-11111-1-1-11i−i
χ311111-1-1-1-1−i−i−i−iiiii-1-1111-1-11−i−iii−i−iii-1-111-1-1111-1−iiii−i−iii−i−iiiii−i−i−i−i-1-1-1-11111-1111-1-1-11−i−iiii−i−i−iiii−i−i−iii11-1-111-1-1-11i−i
χ321111-1-1-1-1−i−i−i−iiiii-1-1111-1-11−i−iii−i−iii-1-111-1-1111-1−iiii−i−iii−i−i−i−i−i−iiiii1111-1-1-1-1-1111-1-1-11ii−i−ii−i−i−iiii−iii−i−i-1-111-1-1111-1−ii
χ332222222222222222222-2-2-2-222222-2-2-2-222220000-2-2-2-2222200000000000000000000-200-200000000-2-20000000000000000000000
χ342222222222222222222-2-2-2-222222-2-2-2-2-2-2-2-20000-2-2-2-2-2-2-2-200000000000000000000200200000000220000000000000000000000
χ352222222222222222-2-2-22222-2-2-2-2-2222200002222-2-2-2-2000022220000000000000000000000-2-20000000000-2-20000000000000000
χ362222222222222222-2-2-22222-2-2-2-2-222220000-2-2-2-2-2-2-2-20000-2-2-2-20000000000000000000000220000000000220000000000000000
χ372222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000002-202-2000000002-22-2000000000000000000
χ382222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000-220-2200000000-22-22000000000000000000
χ3922222222-2-2-2-2-2-2-2-2222-2-2-2-22-2-2-2-2222222220000-2-222-2-2-2-200000000000000000000-200-200000000220000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2222-2-2-2-22-2-2-2-22222-2-2-2-20000-2-222222200000000000000000000200200000000-2-20000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-2-2-22222-22222-2-2-2-200002222-2-2220000-2-2-2-20000000000000000000000-2-20000000000220000000000000000
χ4222222222-2-2-2-2-2-2-2-2-2-2-22222-22222-2-2-2-20000-2-2-2-2-2-222000022220000000000000000000000220000000000-2-20000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000022-2-200000000000000000000000002-202-200000000-22-22000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000022-2-20000000000000000000000000-220-22000000002-22-2000000000000000000
χ452222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-222-2-2-2−2i−2i2i2i2i2i−2i−2i000022-2-2-22−2i2i00002i2i−2i−2i0000000000000000000000-220000000000−2i2i0000000000000000
χ462222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-222-2-2-2−2i−2i2i2i2i2i−2i−2i0000-2-222-22−2i2i0000−2i−2i2i2i00000000000000000000002-200000000002i−2i0000000000000000
χ472222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-2-222-2−2i−2i2i2i−2i−2i2i2i000000002-22i−2i00000000000000000000000002-20-22000000002i−2i−2i2i000000000000000000
χ482222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-2-222-2−2i−2i2i2i−2i−2i2i2i000000002-22i−2i0000000000000000000000000-2202-200000000−2i2i2i−2i000000000000000000
χ492222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-22-2-22222i2i−2i−2i−2i−2i2i2i22-2-20000-22−2i2i2i2i−2i−2i00000000000000000000-200200000000−2i2i0000000000000000000000
χ502222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-22-2-22222i2i−2i−2i−2i−2i2i2i-2-2220000-22−2i2i−2i−2i2i2i00000000000000000000200-2000000002i−2i0000000000000000000000
χ512222-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-222-2-2-22i2i−2i−2i−2i−2i2i2i000022-2-2-222i−2i0000−2i−2i2i2i0000000000000000000000-2200000000002i−2i0000000000000000
χ522222-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-222-2-2-22i2i−2i−2i−2i−2i2i2i0000-2-222-222i−2i00002i2i−2i−2i00000000000000000000002-20000000000−2i2i0000000000000000
χ532222-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-2-222-22i2i−2i−2i2i2i−2i−2i000000002-2−2i2i00000000000000000000000002-20-2200000000−2i2i2i−2i000000000000000000
χ542222-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-2-222-22i2i−2i−2i2i2i−2i−2i000000002-2−2i2i0000000000000000000000000-2202-2000000002i−2i−2i2i000000000000000000
χ552222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-22-2-2222−2i−2i2i2i2i2i−2i−2i22-2-20000-222i−2i−2i−2i2i2i00000000000000000000-2002000000002i−2i0000000000000000000000
χ562222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-22-2-2222−2i−2i2i2i2i2i−2i−2i-2-2220000-222i−2i2i2i−2i−2i00000000000000000000200-200000000−2i2i0000000000000000000000
χ5722-2-222-2-222-2-222-2-2-22-2000022-22-200002i−2i2i−2i000000002i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000002−22−22−22−200000000
χ5822-2-222-2-222-2-222-2-2-22-2000022-22-200002i−2i2i−2i000000002i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000−22−22−22−2200000000
χ5922-2-222-2-222-2-222-2-2-22-2000022-22-20000−2i2i−2i2i00000000−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000−22−22−22−2200000000
χ6022-2-222-2-222-2-222-2-2-22-2000022-22-20000−2i2i−2i2i00000000−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000002−22−22−22−200000000
χ6122-2-222-2-2-2-222-2-222-22-200002-22-2200002i−2i2i−2i00000000−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000002−22−2−22−2200000000
χ6222-2-222-2-2-2-222-2-222-22-200002-22-2200002i−2i2i−2i00000000−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000−22−222−22−200000000
χ6322-2-222-2-2-2-222-2-222-22-200002-22-220000−2i2i−2i2i000000002i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000−22−222−22−200000000
χ6422-2-222-2-2-2-222-2-222-22-200002-22-220000−2i2i−2i2i000000002i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000002−22−2−22−2200000000
χ6522-2-2-2-2222i2i−2i−2i−2i−2i2i2i2-2-2000022i−2i−2i2i00002i−2i−2i2i00000000-222-2000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i2−222−200000000
χ6622-2-2-2-2222i2i−2i−2i−2i−2i2i2i2-2-2000022i−2i−2i2i00002i−2i−2i2i00000000-222-20000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i22−2−2200000000
χ6722-2-2-2-2222i2i−2i−2i−2i−2i2i2i2-2-2000022i−2i−2i2i0000−2i2i2i−2i000000002-2-22000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i22−2−2200000000
χ6822-2-2-2-2222i2i−2i−2i−2i−2i2i2i2-2-2000022i−2i−2i2i0000−2i2i2i−2i000000002-2-220000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i2−222−200000000
χ6922-2-2-2-222−2i−2i2i2i2i2i−2i−2i2-2-200002−2i2i2i−2i00002i−2i−2i2i000000002-2-22000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i22−2−2200000000
χ7022-2-2-2-222−2i−2i2i2i2i2i−2i−2i2-2-200002−2i2i2i−2i00002i−2i−2i2i000000002-2-220000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i2−222−200000000
χ7122-2-2-2-222−2i−2i2i2i2i2i−2i−2i2-2-200002−2i2i2i−2i0000−2i2i2i−2i00000000-222-2000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i2−222−200000000
χ7222-2-2-2-222−2i−2i2i2i2i2i−2i−2i2-2-200002−2i2i2i−2i0000−2i2i2i−2i00000000-222-20000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i22−2−2200000000
χ732-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30002-22i−2i000002ζ−2ζ2ζ3−2ζ300002-22i−2i000000002ζ−2ζ2ζ3−2ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i2−22−2i2−i2i2−i2000000001+i−1−i1−i−1+i00000000000000002−2i2−i20000
χ742-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30002-22i−2i000002ζ−2ζ2ζ3−2ζ300002-22i−2i000000002ζ−2ζ2ζ3−2ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i−22−22−i2i2−i2i200000000−1−i1+i−1+i1−i0000000000000000−22−i2i20000
χ752-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30002-22i−2i000002ζ−2ζ2ζ3−2ζ30000-22−2i2i00000000−2ζ2ζ−2ζ32ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i2−22−2i2−i2i2−i200000000−1−i1+i−1+i1−i0000000000000000−22−i2i20000
χ762-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30002-22i−2i000002ζ−2ζ2ζ3−2ζ30000-22−2i2i00000000−2ζ2ζ−2ζ32ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i−22−22−i2i2−i2i2000000001+i−1−i1−i−1+i00000000000000002−2i2−i20000
χ772-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30002-22i−2i00000−2ζ2ζ−2ζ32ζ300002-22i−2i00000000−2ζ2ζ−2ζ32ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i−22−22−i2i2−i2i2000000001+i−1−i1−i−1+i0000000000000000−22−i2i20000
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χ1044-4-44−4i4i4i−4i−4ζ34ζ34ζ3−4ζ3−4ζ4ζ4ζ−4ζ000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2i2i2i−2i-222-2000000000000000000000000000000000000

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