Finite Group Databasebeta

← Group #138658

Character table — Group #138658

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order12222244448888888816161616161616164444888816161616161616161616161622448888161616161616161616161616161616162244
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91-11-1-11-1-1111111-1-1-1-1iiii−i−i−i−i11-1-11-11-1ii−i−iiiii−i−i−i−i1-11-111-1-1iiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101-11-1-11-1-1111111-1-1-1-1iiii−i−i−i−i11-1-11-11-1ii−i−iiiii−i−i−i−i1-11-111-1-1iiii−i−i−i−i-1-111−i−iii-11−ii
χ111-11-1-11-1-1111111-1-1-1-1iiii−i−i−i−i11-1-11-11-1ii−i−iiiii−i−i−i−i-11-11-1-111−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121-11-1-11-1-1111111-1-1-1-1iiii−i−i−i−i11-1-11-11-1ii−i−iiiii−i−i−i−i-11-11-1-111−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131-11-1-11-1-1111111-1-1-1-1−i−i−i−iiiii11-1-11-11-1−i−iii−i−i−i−iiiii1-11-111-1-1−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141-11-1-11-1-1111111-1-1-1-1−i−i−i−iiiii11-1-11-11-1−i−iii−i−i−i−iiiii1-11-111-1-1−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151-11-1-11-1-1111111-1-1-1-1−i−i−i−iiiii11-1-11-11-1−i−iii−i−i−i−iiiii-11-11-1-111iiii−i−i−i−i11-1-1−i−iii-11i−i
χ161-11-1-11-1-1111111-1-1-1-1−i−i−i−iiiii11-1-11-11-1−i−iii−i−i−i−iiiii-11-11-1-111iiii−i−i−i−i-1-111ii−i−i1-1−ii
χ17222222222222-2-2-2-22222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222220000000000000000000000000000
χ192222222222-2-22222-2-200000000-2-2-2-222-2-20000000000002222-2-2-2-200000000000000000000
χ202222222222-2-22222-2-200000000-2-2-2-222-2-2000000000000-2-2-2-2222200000000000000000000
χ212222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ232222-2-22-22-20022220022−2−222−2−20000-2-2002−22−222−2−222−2−222-2-200002−22−22−22−2000000000000
χ242222-2-22-22-20022220022−2−222−2−20000-2-2002−22−222−2−222−2−2-2-2220000−22−22−22−22000000000000
χ252222-2-22-22-200222200−2−222−2−2220000-2-200−22−22−2−222−2−22222-2-20000−22−22−22−22000000000000
χ262222-2-22-22-200222200−2−222−2−2220000-2-200−22−22−2−222−2−222-2-22200002−22−22−22−2000000000000
χ272222-2-22-22-200-2-2-2-20022−2−222−2−2000022002−22−2−2−222−2−22200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i2000000000000
χ282222-2-22-22-200-2-2-2-20022−2−222−2−2000022002−22−2−2−222−2−2220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i2000000000000
χ292222-2-22-22-200-2-2-2-200−2−222−2−22200002200−22−2222−2−222−2−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2000000000000
χ302222-2-22-22-200-2-2-2-200−2−222−2−22200002200−22−2222−2−222−2−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2000000000000
χ312222-2-2-22-222200002222222222000000-2-2-2-2-2-20000000000000000000000002−22−22−22−20000
χ322222-2-2-22-222200002222222222000000-2-2-2-2-2-2000000000000000000000000−22−22−22−220000
χ332222-2-2-22-2222000022-2-2-2-2-2-2-2-2000000-2-222220000000000000000000000002−22−2−22−220000
χ342222-2-2-22-2222000022-2-2-2-2-2-2-2-2000000-2-22222000000000000000000000000−22−222−22−20000
χ352-22-22-22-2-22220000-2-22i2i2i2i−2i−2i−2i−2i000000-22−2i−2i2i2i0000000000000000000000002−2−22i2−i2−i2i20000
χ362-22-22-22-2-22220000-2-22i2i2i2i−2i−2i−2i−2i000000-22−2i−2i2i2i000000000000000000000000−222−2−i2i2i2−i20000
χ372-22-22-22-2-22220000-2-2−2i−2i−2i−2i2i2i2i2i000000-222i2i−2i−2i0000000000000000000000002−2−22−i2i2i2−i20000
χ382-22-22-22-2-22220000-2-2−2i−2i−2i−2i2i2i2i2i000000-222i2i−2i−2i000000000000000000000000−222−2i2−i2−i2i20000
χ392-22-22-2-222-20022-2-200i2i2−i2−i2−i2−i2i2i20000-2200i2−i2−i2i2i2i2−i2−i2−i2−i2i2i22-2-220000i2−i2i2−i2−i2i2−i2i2000000000000
χ402-22-22-2-222-20022-2-200i2i2−i2−i2−i2−i2i2i20000-2200i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2-222-20000−i2i2−i2i2i2−i2i2−i2000000000000
χ412-22-22-2-222-20022-2-200−i2−i2i2i2i2i2−i2−i20000-2200−i2i2i2−i2−i2−i2i2i2i2i2−i2−i22-2-220000−i2i2−i2i2i2−i2i2−i2000000000000
χ422-22-22-2-222-20022-2-200−i2−i2i2i2i2i2−i2−i20000-2200−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2-222-20000i2−i2i2−i2−i2i2−i2i2000000000000
χ432-22-22-2-222-200-2-22200i2i2−i2−i2−i2−i2i2i200002-200i2−i2−i2i2−i2−i2i2i2i2i2−i2−i200002i−2i−2i2i−222−22−2−22000000000000
χ442-22-22-2-222-200-2-22200i2i2−i2−i2−i2−i2i2i200002-200i2−i2−i2i2−i2−i2i2i2i2i2−i2−i20000−2i2i2i−2i2−2−22−222−2000000000000
χ452-22-22-2-222-200-2-22200−i2−i2i2i2i2i2−i2−i200002-200−i2i2i2−i2i2i2−i2−i2−i2−i2i2i200002i−2i−2i2i2−2−22−222−2000000000000
χ462-22-22-2-222-200-2-22200−i2−i2i2i2i2i2−i2−i200002-200−i2i2i2−i2i2i2−i2−i2−i2−i2i2i20000−2i2i2i−2i−222−22−2−22000000000000
χ472-22-2-22-2-22222-2-222-2-22i2i2i2i−2i−2i−2i−2i-2-222-222-22i2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ482-22-2-22-2-22222-2-222-2-2−2i−2i−2i−2i2i2i2i2i-2-222-222-2−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ492-22-2-22-2-222-2-222-2-22200000000-2-2222-2-220000000000002-22-2-2-22200000000000000000000
χ502-22-2-22-2-222-2-222-2-22200000000-2-2222-2-22000000000000-22-2222-2-200000000000000000000
χ512-22-2-22-2-222-2-2-2-222220000000022-2-2-22-220000000000000000000022-2-2-2-222000000000000
χ522-22-2-22-2-222-2-2-2-222220000000022-2-2-22-2200000000000000000000-2-22222-2-2000000000000
χ53444444-4-4-4-4000000002222−22−222222−22−2200000000−2222−2222000000000000000000000000000000000000
χ54444444-4-4-4-400000000−22−222222−22−2222220000000022−2222−22000000000000000000000000000000000000
χ554444-4-4-44-44-4-40000-4-400000000000000440000000000000000000000000000000000000000
χ5644-4-400000022−2222−2222−2222−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52-22-200000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ70000000000000000000000000000
χ5744-4-400000022−2222−2222−2222−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52-22-200000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ70000000000000000000000000000
χ5844-4-400000022−22−2222−222222−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5-22-2200000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ70000000000000000000000000000
χ5944-4-400000022−22−2222−222222−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5-22-2200000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ70000000000000000000000000000
χ6044-4-4000000−222222−2222−22−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7-22-2200000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ70000000000000000000000000000
χ6144-4-4000000−222222−2222−22−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7-22-2200000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ70000000000000000000000000000
χ6244-4-4000000−2222−2222−2222−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72-22-200000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ70000000000000000000000000000
χ6344-4-4000000−2222−2222−2222−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72-22-200000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ70000000000000000000000000000
χ644-44-44-44-4-44-4-4000044000000000000004-40000000000000000000000000000000000000000
χ654-44-4-4444-4-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000−2i22i22i2−2i2000000000000000000000000000000000000
χ664-44-4-4444-4-400000000−2i2−2i22i22i22i22i2−2i2−2i2000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ674-4-4400000022−2222−22−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72-2-2200000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000000000000000000
χ684-4-4400000022−2222−22−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72-2-2200000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000000000000000000
χ694-4-4400000022−22−222222−22−22222ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7-222-200000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000000000000000000
χ704-4-4400000022−22−222222−22−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7-222-200000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000000000000000000
χ714-4-44000000−222222−22−222222−222ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5-222-200000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ70000000000000000000000000000
χ724-4-44000000−222222−22−222222−22−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5-222-200000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ70000000000000000000000000000
χ734-4-44000000−2222−222222−2222−222ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52-2-2200000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ70000000000000000000000000000
χ744-4-44000000−2222−222222−2222−22−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52-2-2200000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ70000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.