Finite Group Databasebeta

← Group #490874

Character table — Group #490874

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order122222444444448888888888884488888888888888888816161616161616161616161616161616224488884444
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
χ5111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-11111-1-1-1-111111111-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-11-11-1
χ101111-1-1-1-1-1-11111-1-1-1-111111111-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-11-11
χ111111-1-1-1-1-1-11111-1-1-1-111111111-1111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-11-11
χ121111-1-1-1-1-1-11111-1-1-1-111111111-1111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1111-11-1
χ131111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-1111-1-11
χ141111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1111-1-1-111-1
χ151111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-1-111-111-1
χ161111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-11-1-11
χ1722222222222222-2-2-2-22222-2-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ1922222222-2-22-2-22000022220000-2-20000-2-2-2-2220000000022−2−222−2−222−2−222−2−2000000000000
χ2022222222-2-22-2-22000022220000-2-20000-2-2-2-22200000000−2−222−2−222−2−222−2−222000000000000
χ2122222222-2-22-2-220000-2-2-2-20000-2-200002222-2-20000000022−2−222−2−2−2−222−2−222000000000000
χ2222222222-2-22-2-220000-2-2-2-20000-2-200002222-2-200000000−2−222−2−22222−2−222−2−2000000000000
χ23222222-2-2-2-2-222-222220000-2-2-2-22-222-2-200000000000000000000000000000000002i−2i2i−2i0000
χ24222222-2-2-2-2-222-222220000-2-2-2-22-222-2-20000000000000000000000000000000000−2i2i−2i2i0000
χ25222222-2-2-2-2-222-2-2-2-2-2000022222-2-2-2220000000000000000000000000000002-2-2200000000
χ26222222-2-2-2-2-222-2-2-2-2-2000022222-2-2-222000000000000000000000000000000-222-200000000
χ272222-2-22222-222-2222200002222-2-2-2-2-2-200000000000000000000000000000022-2-200000000
χ282222-2-22222-222-2222200002222-2-2-2-2-2-2000000000000000000000000000000-2-22200000000
χ292222-2-22222-222-2-2-2-2-20000-2-2-2-2-2-2222200000000000000000000000000000000002i−2i−2i2i0000
χ302222-2-22222-222-2-2-2-2-20000-2-2-2-2-2-222220000000000000000000000000000000000−2i2i2i−2i0000
χ312222-2-2-2-2222-2-220000222200002-20000-2-222-2-20000000022−2−2−2−22222−2−2−2−222000000000000
χ322222-2-2-2-2222-2-220000222200002-20000-2-222-2-200000000−2−22222−2−2−2−22222−2−2000000000000
χ332222-2-2-2-2222-2-220000-2-2-2-200002-2000022-2-2220000000022−2−2−2−222−2−22222−2−2000000000000
χ342222-2-2-2-2222-2-220000-2-2-2-200002-2000022-2-22200000000−2−22222−2−222−2−2−2−222000000000000
χ352222-2-2-2-2-2-2222222222222-2-2-2-2-22-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ362222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-22-2-222-2-222222222-2-2-2-20000000000000000000000000000
χ3722-2-22-22-200-200222−2−222-2-222−2−2002−22−200002-222−2−222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3822-2-22-22-200-200222−2−222-2-222−2−2002−22−200002-222−2−222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3922-2-22-22-200-200222−2−2-2-22222−2−2002−22−20000-22−2−222−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4022-2-22-22-200-200222−2−2-2-22222−2−2002−22−20000-22−2−222−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4122-2-22-22-200-2002−2−22222-2-2−2−22200−22−2200002-2−2−222−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ4222-2-22-22-200-2002−2−22222-2-2−2−22200−22−2200002-2−2−222−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ4322-2-22-22-200-2002−2−222-2-222−2−22200−22−220000-2222−2−222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ4422-2-22-22-200-2002−2−222-2-222−2−22200−22−220000-2222−2−222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ4522-2-2-22-2200-200222−2−222-2-2−2−22200−222−20000-22−2−22222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ4622-2-2-22-2200-200222−2−222-2-2−2−22200−222−20000-22−2−22222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ4722-2-2-22-2200-200222−2−2-2-222−2−22200−222−200002-222−2−2−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ4822-2-2-22-2200-200222−2−2-2-222−2−22200−222−200002-222−2−2−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ4922-2-2-22-2200-2002−2−22222-2-222−2−2002−2−220000-2222−2−2−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ5022-2-2-22-2200-2002−2−22222-2-222−2−2002−2−220000-2222−2−2−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ5122-2-2-22-2200-2002−2−222-2-22222−2−2002−2−2200002-2−2−22222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ5222-2-2-22-2200-2002−2−222-2-22222−2−2002−2−2200002-2−2−22222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ53444444-4-444-4-4-4-4000000000000-440000000000000000000000000000000000000000000000
χ544444-4-444-4-4-4-4-4-4000000000000440000000000000000000000000000000000000000000000
χ5544-4-44-4-4400400-42222−22−220000−22−2222220022−22−2222000000000000000000000000000000000000000000
χ5644-4-44-4-4400400-4−22−22222200002222−22−2200−222222−22000000000000000000000000000000000000000000
χ5744-4-4-444-400400-42222−22−2200002222−22−2200−2222−2222000000000000000000000000000000000000000000
χ5844-4-4-444-400400-4−22−2222220000−22−2222220022−2222−22000000000000000000000000000000000000000000
χ594-44-400000004-4000002i2−2i22i2−2i24-44-40000002i2−2i200002i2−2i22i2−2i200000000000000000000000000000000
χ604-44-400000004-4000002i2−2i22i2−2i2-44-440000002i2−2i20000−2i22i2−2i22i200000000000000000000000000000000
χ614-44-400000004-400000−2i22i2−2i22i24-44-4000000−2i22i20000−2i22i2−2i22i200000000000000000000000000000000
χ624-44-400000004-400000−2i22i2−2i22i2-44-44000000−2i22i200002i2−2i22i2−2i200000000000000000000000000000000
χ634-44-40000000-4404-44-42i2−2i22i2−2i20000000000−2i22i2000000002i2−2i22i2−2i20000000000000000000000000000
χ644-44-40000000-4404-44-4−2i22i2−2i22i200000000002i2−2i200000000−2i22i2−2i22i20000000000000000000000000000
χ654-44-40000000-440-44-442i2−2i22i2−2i20000000000−2i22i200000000−2i22i2−2i22i20000000000000000000000000000
χ664-44-40000000-440-44-44−2i22i2−2i22i200000000002i2−2i2000000002i2−2i22i2−2i20000000000000000000000000000
χ674-4-4400004-4000022−22−22222i2−2i2−2i22i222−22−2222000000002i2−2i2002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ684-4-4400004-4000022−22−2222−2i22i22i2−2i222−22−222200000000−2i22i200−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ694-4-4400004-40000−222222−222i2−2i2−2i22i2−222222−22000000002i2−2i200−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ704-4-4400004-40000−222222−22−2i22i22i2−2i2−222222−2200000000−2i22i2002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ714-4-440000-44000022−22−22222i2−2i2−2i22i2−222222−2200000000−2i22i200−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ724-4-440000-44000022−22−2222−2i22i22i2−2i2−222222−22000000002i2−2i2002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ734-4-440000-440000−222222−222i2−2i2−2i22i222−22−222200000000−2i22i2002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ744-4-440000-440000−222222−22−2i22i22i2−2i222−22−2222000000002i2−2i200−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000

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