Finite Group Databasebeta

← Group #490976

Character table — Group #490976

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order122222444444448888888888884488888888888888888816161616161616161616161616161616444488882244
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
χ511111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ611111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111-1-1-1-1-1-1111111-1-1-1-1111111-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111-1-1-1-1-1-1111111-1-1-1-1111111-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ111111-1-1-1-1-1-1111111-1-1-1-1111111-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ121111-1-1-1-1-1-1111111-1-1-1-1111111-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ131111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ161111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222-2-2-2-2-2-22222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ1922222222-2-222-2-2222222000022-2-2-2-2-2-20000000000000000000000000000002-22-200000000
χ2022222222-2-222-2-2222222000022-2-2-2-2-2-2000000000000000000000000000000-22-2200000000
χ2122222222-2-222-2-2-2-2-2-2-2-20000-2-2-2-2222200000000000000000000000000000000002i−2i2i−2i0000
χ2222222222-2-222-2-2-2-2-2-2-2-20000-2-2-2-222220000000000000000000000000000000000−2i2i−2i2i0000
χ23222222-2-222-2-222000000222200-2-2000022-2-2-2-20000000022−2−222−2−222−2−222−2−2000000000000
χ24222222-2-222-2-222000000222200-2-2000022-2-2-2-200000000−2−222−2−222−2−222−2−222000000000000
χ25222222-2-222-2-222000000-2-2-2-200-2-20000-2-222220000000022−2−222−2−2−2−222−2−222000000000000
χ26222222-2-222-2-222000000-2-2-2-200-2-20000-2-2222200000000−2−222−2−22222−2−222−2−2000000000000
χ272222-2-222-2-2-2-2220000002222002-20000-2-2-2-2220000000022−2−2−2−22222−2−2−2−222000000000000
χ282222-2-222-2-2-2-2220000002222002-20000-2-2-2-22200000000−2−22222−2−2−2−22222−2−2000000000000
χ292222-2-222-2-2-2-222000000-2-2-2-2002-200002222-2-20000000022−2−2−2−222−2−22222−2−2000000000000
χ302222-2-222-2-2-2-222000000-2-2-2-2002-200002222-2-200000000−2−22222−2−222−2−2−2−222000000000000
χ312222-2-2-2-22222-2-222-2-2-2-20000222-2-2-2220000000000000000000000000000002-2-2200000000
χ322222-2-2-2-22222-2-222-2-2-2-20000222-2-2-222000000000000000000000000000000-222-200000000
χ332222-2-2-2-22222-2-2-2-222220000-2-22-222-2-200000000000000000000000000000000002i−2i−2i2i0000
χ342222-2-2-2-22222-2-2-2-222220000-2-22-222-2-20000000000000000000000000000000000−2i2i2i−2i0000
χ352222-2-2-2-2-2-22222-2-222222222-2-2-22-2-222-2-222-2-2-2-2-2-222220000000000000000000000000000
χ362222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-22-2-22222-2-2222222-2-2-2-20000000000000000000000000000
χ372-2-222-2002-2002-22−222−2−222-2-22−2002−22−22-2000022−2−222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ382-2-222-2002-2002-22−222−2−222-2-22−2002−22−22-2000022−2−222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ392-2-222-2002-2002-22−222−2−2-2-2222−2002−22−2-220000−2−222−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ402-2-222-2002-2002-22−222−2−2-2-2222−2002−22−2-220000−2−222−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ412-2-222-2002-2002-2−22−2−22222-2-2−2200−22−222-20000−2−222−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ422-2-222-2002-2002-2−22−2−22222-2-2−2200−22−222-20000−2−222−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ432-2-222-2002-2002-2−22−2−222-2-222−2200−22−22-22000022−2−222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ442-2-222-2002-2002-2−22−2−222-2-222−2200−22−22-22000022−2−222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ452-2-22-2200-22002-22−2−2−22222-2-22−2002−2−22-22000022−2−2−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ462-2-22-2200-22002-22−2−2−22222-2-22−2002−2−22-22000022−2−2−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ472-2-22-2200-22002-22−2−2−222-2-2222−2002−2−222-20000−2−22222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ482-2-22-2200-22002-22−2−2−222-2-2222−2002−2−222-20000−2−22222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ492-2-22-2200-22002-2−2222−2−222-2-2−2200−222−2-220000−2−22222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ502-2-22-2200-22002-2−2222−2−222-2-2−2200−222−2-220000−2−22222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ512-2-22-2200-22002-2−2222−2−2-2-222−2200−222−22-2000022−2−2−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ522-2-22-2200-22002-2−2222−2−2-2-222−2200−222−22-2000022−2−2−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ53444444-4-4-4-4-4-4-4-4000000000000440000000000000000000000000000000000000000000000
χ544444-4-44444-4-4-4-4000000000000-440000000000000000000000000000000000000000000000
χ5544-4-40000004-400004i−4i4i−4i22−2222−22000000000022−220000002i2−2i22i2−2i20000000000000000000000000000
χ5644-4-40000004-400004i−4i4i−4i−2222−22220000000000−2222000000−2i22i2−2i22i20000000000000000000000000000
χ5744-4-40000004-40000−4i4i−4i4i22−2222−22000000000022−22000000−2i22i2−2i22i20000000000000000000000000000
χ5844-4-40000004-40000−4i4i−4i4i−2222−22220000000000−22220000002i2−2i22i2−2i20000000000000000000000000000
χ5944-4-4000000-440044000022−2222−22-4-400000000−22220022−2222−2200000000000000000000000000000000
χ6044-4-4000000-4400440000−2222−2222-4-40000000022−2200−2222−222200000000000000000000000000000000
χ6144-4-4000000-4400-4-4000022−2222−224400000000−222200−2222−222200000000000000000000000000000000
χ6244-4-4000000-4400-4-40000−2222−2222440000000022−220022−2222−2200000000000000000000000000000000
χ634-44-4004i−4i00000022−222i2−2i2−2i22i222−22−2222−222200000000002i2−2i22-2-222i−2i−2i2i0000000000000000000000000000
χ644-44-4004i−4i00000022−222i2−2i2−2i22i2−222222−22−22220000000000−2i22i2-222-2−2i2i2i−2i0000000000000000000000000000
χ654-44-4004i−4i000000−2222−2i22i22i2−2i222−22−222222−2200000000002i2−2i2-222-2−2i2i2i−2i0000000000000000000000000000
χ664-44-4004i−4i000000−2222−2i22i22i2−2i2−222222−2222−220000000000−2i22i22-2-222i−2i−2i2i0000000000000000000000000000
χ674-44-400−4i4i00000022−22−2i22i22i2−2i222−22−2222−22220000000000−2i22i22-2-22−2i2i2i−2i0000000000000000000000000000
χ684-44-400−4i4i00000022−22−2i22i22i2−2i2−222222−22−222200000000002i2−2i2-222-22i−2i−2i2i0000000000000000000000000000
χ694-44-400−4i4i000000−22222i2−2i2−2i22i222−22−222222−220000000000−2i22i2-222-22i−2i−2i2i0000000000000000000000000000
χ704-44-400−4i4i000000−22222i2−2i2−2i22i2−222222−2222−2200000000002i2−2i22-2-22−2i2i2i−2i0000000000000000000000000000
χ714-4-444-400-4400-4422−222222−22−22000022−2200−2222−2222000000000000000000000000000000000000000000
χ724-4-444-400-4400-44−2222−22−2222220000−22220022−2222−22000000000000000000000000000000000000000000
χ734-4-44-44004-400-4422−22−22−222222000022−2200−222222−22000000000000000000000000000000000000000000
χ744-4-44-44004-400-44−22222222−22−220000−22220022−22−2222000000000000000000000000000000000000000000

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