Finite Group Databasebeta

← Group #148317

Character table — Group #148317

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222222444444888888888888161616161616161616161616161616162244888816161616161616164444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ192222222222-2-2-2-22-2-2-2-22-2-2-2-2-2-2-2-2222200000000000000002-22-2-2-222000000000000000000000000
χ202222222222-2-2-2-22-2-2-2-22-2-2-2-2-2-2-2-222220000000000000000-22-2222-2-2000000000000000000000000
χ2122222222-2-22-2-22-222-2-2-20000000000002222−2−2−2−22222−2−2−2−200002i−2i2i−2ii2i2−i2−i2i2i2−i2−i20000000000000000
χ2222222222-2-22-2-22-222-2-2-20000000000002222−2−2−2−22222−2−2−2−20000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i20000000000000000
χ2322222222-2-22-2-22-222-2-2-2000000000000−2−2−2−22222−2−2−2−2222200002i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000000000000000
χ2422222222-2-22-2-22-222-2-2-2000000000000−2−2−2−22222−2−2−2−222220000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000000000000000
χ2522222222-2-2-222-2-2-2-222-20000000000002222−2−2−2−2−2−2−2−2222200002i−2i−2i2ii2i2−i2−i2−i2−i2i2i20000000000000000
χ2622222222-2-2-222-2-2-2-222-20000000000002222−2−2−2−2−2−2−2−222220000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20000000000000000
χ2722222222-2-2-222-2-2-2-222-2000000000000−2−2−2−222222222−2−2−2−200002i−2i−2i2i−i2−i2i2i2i2i2−i2−i20000000000000000
χ2822222222-2-2-222-2-2-2-222-2000000000000−2−2−2−222222222−2−2−2−20000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20000000000000000
χ292222-2-2-2-2222222-2-2-2-2-2-200000000000022−2−222−2−222−2−222−2−22-2-2200002−22−22−22−20000000000000000
χ302222-2-2-2-2222222-2-2-2-2-2-200000000000022−2−222−2−222−2−222−2−2-222-20000−22−22−22−220000000000000000
χ312222-2-2-2-2222222-2-2-2-2-2-2000000000000−2−222−2−222−2−222−2−2222-2-220000−22−22−22−220000000000000000
χ322222-2-2-2-2222222-2-2-2-2-2-2000000000000−2−222−2−222−2−222−2−222-222-200002−22−22−22−20000000000000000
χ332222-2-2-2-222-2-2-2-2-22222-200000000000022−2−222−2−2−2−222−2−22222-2-200002−22−2−22−220000000000000000
χ342222-2-2-2-222-2-2-2-2-22222-200000000000022−2−222−2−2−2−222−2−222-2-2220000−22−222−22−20000000000000000
χ352222-2-2-2-222-2-2-2-2-22222-2000000000000−2−222−2−22222−2−222−2−222-2-20000−22−222−22−20000000000000000
χ362222-2-2-2-222-2-2-2-2-22222-2000000000000−2−222−2−22222−2−222−2−2-2-22200002−22−2−22−220000000000000000
χ372222-2-2-2-2-2-22-2-222-2-22222222-2-2-2-222-2-20000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ382222-2-2-2-2-2-22-2-222-2-22222222-2-2-2-222-2-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ392222-2-2-2-2-2-22-2-222-2-2222-2-2-2-22222-2-22222-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ402222-2-2-2-2-2-22-2-222-2-2222-2-2-2-22222-2-222-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ412222-2-2-2-2-2-2-222-2222-2-222222-2-2-2-2-2-2220000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ422222-2-2-2-2-2-2-222-2222-2-222222-2-2-2-2-2-222000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ432222-2-2-2-2-2-2-222-2222-2-22-2-2-2-2222222-2-222-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ442222-2-2-2-2-2-2-222-2222-2-22-2-2-2-2222222-2-2-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ452-2-2222-2-22-222-2-2-22-22-2222-2-222-2-22-22-2000000000000000000000000000000000000000000002i−2i2i−2i
χ462-2-2222-2-22-222-2-2-22-22-2222-2-222-2-22-22-200000000000000000000000000000000000000000000−2i2i−2i2i
χ472-2-2222-2-22-222-2-2-22-22-22-2-222-2-222-22-220000000000000000000000000000000000002i−2i2i−2i00000000
χ482-2-2222-2-22-222-2-2-22-22-22-2-222-2-222-22-22000000000000000000000000000000000000−2i2i−2i2i00000000
χ492-2-2222-2-22-2-2-222-2-22-22222-2-222-2-2-22-22000000000000000000000000000000000000000000002-2-22
χ502-2-2222-2-22-2-2-222-2-22-22222-2-222-2-2-22-2200000000000000000000000000000000000000000000-222-2
χ512-2-2222-2-22-2-2-222-2-22-222-2-222-2-2222-22-20000000000000000000000000000000000002-2-2200000000
χ522-2-2222-2-22-2-2-222-2-22-222-2-222-2-2222-22-2000000000000000000000000000000000000-222-200000000
χ532-2-22-2-222-222-22-2-2-222-2222-2-2-2-2222-2-22000000000000000000000000000000002i−2i2i−2i000000000000
χ542-2-22-2-222-222-22-2-2-222-2222-2-2-2-2222-2-2200000000000000000000000000000000−2i2i−2i2i000000000000
χ552-2-22-2-222-222-22-2-2-222-22-2-22222-2-2-222-200000000000000000000000000000000000000002i−2i2i−2i0000
χ562-2-22-2-222-222-22-2-2-222-22-2-22222-2-2-222-20000000000000000000000000000000000000000−2i2i−2i2i0000
χ572-2-22-2-222-22-22-22-22-2-22222-2-2-2-222-222-2000000000000000000000000000000002-2-22000000000000
χ582-2-22-2-222-22-22-22-22-2-22222-2-2-2-222-222-200000000000000000000000000000000-222-2000000000000
χ592-2-22-2-222-22-22-22-22-2-222-2-22222-2-22-2-2200000000000000000000000000000000000000002-2-220000
χ602-2-22-2-222-22-22-22-22-2-222-2-22222-2-22-2-220000000000000000000000000000000000000000-222-20000
χ6144-4-44i−4i4i−4i0000000000002i2−2i22i2−2i222−2222−220000000000002ζ+2ζ7−2ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ6244-4-44i−4i4i−4i0000000000002i2−2i22i2−2i222−2222−22000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ6344-4-44i−4i4i−4i000000000000−2i22i2−2i22i2−2222−22220000000000002ζ3+2ζ5−2ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ6444-4-44i−4i4i−4i000000000000−2i22i2−2i22i2−2222−2222000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ6544-4-4−4i4i−4i4i0000000000002i2−2i22i2−2i2−2222−22220000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ6644-4-4−4i4i−4i4i0000000000002i2−2i22i2−2i2−2222−2222000000000000−2ζ3−2ζ52ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ6744-4-4−4i4i−4i4i000000000000−2i22i2−2i22i222−2222−220000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ6844-4-4−4i4i−4i4i000000000000−2i22i2−2i22i222−2222−22000000000000−2ζ−2ζ72ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ694-44-44i−4i−4i4i0000000000002i2−2i2−2i22i222−22−222200002ζ+2ζ7−2ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000000000000000000
χ704-44-44i−4i−4i4i0000000000002i2−2i2−2i22i222−22−22220000−2ζ−2ζ72ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000000000000000000
χ714-44-44i−4i−4i4i000000000000−2i22i22i2−2i2−222222−2200002ζ3+2ζ5−2ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000000000000000000000
χ724-44-44i−4i−4i4i000000000000−2i22i22i2−2i2−222222−220000−2ζ3−2ζ52ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000000000000000000000
χ734-44-4−4i4i4i−4i0000000000002i2−2i2−2i22i2−222222−2200002ζ3+2ζ5−2ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000000000000000000000
χ744-44-4−4i4i4i−4i0000000000002i2−2i2−2i22i2−222222−220000−2ζ3−2ζ52ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000000000000000000000
χ754-44-4−4i4i4i−4i000000000000−2i22i22i2−2i222−22−222200002ζ+2ζ7−2ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000000000000000000
χ764-44-4−4i4i4i−4i000000000000−2i22i22i2−2i222−22−22220000−2ζ−2ζ72ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000000000000000000
χ774-4-4444-4-4-444-44-444-4-44-4000000000000000000000000000000000000000000000000000000000000
χ784-4-4444-4-4-44-44-444-444-4-4000000000000000000000000000000000000000000000000000000000000
χ794-4-44-4-4444-444-4-44-44-44-4000000000000000000000000000000000000000000000000000000000000
χ804-4-44-4-4444-4-4-44444-44-4-4000000000000000000000000000000000000000000000000000000000000

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