Finite Group Databasebeta

← Group #257358

Character table — Group #257358

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444444444444444888888888888888822244444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11111
χ7111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111
χ8111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111111-111-1-1-1-1
χ91111111111111-1-1-1-1111-1-1-1-1111111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111-1-1-11111-1-1
χ101111111111111-1-1-1-1111-1-1-1-1111111-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-111-111-1-111
χ111111111111111-1-1-1-1111-1-1-1-1111111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-11-1-1-1-111
χ121111111111111-1-1-1-1111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1111-1-111-1-1
χ131111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1-111
χ141111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-111-1-1
χ151111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1
χ161111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-111-1-1111-1-111
χ172222222222-2-2-2222222-2-2-2220000-2-2-222220000000000000000000000-2000000-2000000
χ182222222222-2-2-2222222-2-2-2220000-2-2-2-2-2-2-2000000000000000000000020000002000000
χ192222222222-2-2-2-2-2-2-222-222-2-20000-2-2222-2-20000000000000000000000-20000002000000
χ202222222222-2-2-2-2-2-2-222-222-2-20000-2-22-2-22200000000000000000000002000000-2000000
χ2122222222-2-22222222-2-2222-2-22222-2-2-20000-2-2-2-222000000000000000000000000000000
χ2222222222-2-22222222-2-2222-2-2-2-2-2-2-2-2-200002222-2-2000000000000000000000000000000
χ2322222222-2-2222-2-2-2-2-2-22-2-2222222-2-220000-2-222-2-2000000000000000000000000000000
χ2422222222-2-2222-2-2-2-2-2-22-2-222-2-2-2-2-2-22000022-2-222000000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-200002220000000000000000000000000002-2000002-20000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-20000222000000000000000000000000000-2200000-220000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-20000000000000000000000000002-200000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-2000000000000000000000000000-22000002-20000
χ292222-2-2-2-22-22-2-200002-2200002i2i−2i−2i2-2000002i−2i0000000022-2-200000000000002i−2i0000000
χ302222-2-2-2-22-22-2-200002-2200002i2i−2i−2i2-2000002i−2i00000000-2-2220000000000000−2i2i0000000
χ312222-2-2-2-22-22-2-200002-220000−2i−2i2i2i2-200000−2i2i0000000022-2-20000000000000−2i2i0000000
χ322222-2-2-2-22-22-2-200002-220000−2i−2i2i2i2-200000−2i2i00000000-2-22200000000000002i−2i0000000
χ332222-2-2-2-2-222-2-20000-22200002i2i−2i−2i-2200000−2i2i000022-2-20000000000000002i−2i000000000
χ342222-2-2-2-2-222-2-20000-22200002i2i−2i−2i-2200000−2i2i0000-2-222000000000000000−2i2i000000000
χ352222-2-2-2-2-222-2-20000-2220000−2i−2i2i2i-22000002i−2i000022-2-2000000000000000−2i2i000000000
χ362222-2-2-2-2-222-2-20000-2220000−2i−2i2i2i-22000002i−2i0000-2-2220000000000000002i−2i000000000
χ3722-2-222-2-22-20002i2i−2i−2i-220002i−2i00000002i−2i2-20000002−22−2i2−i2i2−i2i2i2−i2−i222−2−200000000000000
χ3822-2-222-2-22-20002i2i−2i−2i-220002i−2i00000002i−2i2-2000000−22−22−i2i2−i2i2−i2−i2i2i2−2−22200000000000000
χ3922-2-222-2-22-20002i2i−2i−2i-220002i−2i0000000−2i2i-220000002−22−2i2−i2i2−i2−i2−i2i2i2−2−22200000000000000
χ4022-2-222-2-22-20002i2i−2i−2i-220002i−2i0000000−2i2i-22000000−22−22−i2i2−i2i2i2i2−i2−i222−2−200000000000000
χ4122-2-222-2-22-2000−2i−2i2i2i-22000−2i2i00000002i−2i-220000002−22−2−i2i2−i2i2i2i2−i2−i2−2−22200000000000000
χ4222-2-222-2-22-2000−2i−2i2i2i-22000−2i2i00000002i−2i-22000000−22−22i2−i2i2−i2−i2−i2i2i222−2−200000000000000
χ4322-2-222-2-22-2000−2i−2i2i2i-22000−2i2i0000000−2i2i2-20000002−22−2−i2i2−i2i2−i2−i2i2i222−2−200000000000000
χ4422-2-222-2-22-2000−2i−2i2i2i-22000−2i2i0000000−2i2i2-2000000−22−22i2−i2i2−i2i2i2−i2−i2−2−22200000000000000
χ452-2-222-2-220022-22-22-200-22-2002-22-2000000000002-200000000i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i2
χ462-2-222-2-220022-22-22-200-22-2002-22-2000000000002-200000000−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i2
χ472-2-222-2-220022-22-22-200-22-200-22-2200000000000-2200000000i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i2
χ482-2-222-2-220022-22-22-200-22-200-22-2200000000000-2200000000−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i2
χ492-2-222-2-220022-2-22-2200-2-22002-22-200000000000-2200000000i2−i2i2−i2−i2i2−i2i20000000000i2−i2−i2i2
χ502-2-222-2-220022-2-22-2200-2-22002-22-200000000000-2200000000−i2i2−i2i2i2−i2i2−i20000000000−i2i2i2−i2
χ512-2-222-2-220022-2-22-2200-2-2200-22-22000000000002-200000000i2−i2i2−i2−i2i2−i2i20000000000−i2i2i2−i2
χ522-2-222-2-220022-2-22-2200-2-2200-22-22000000000002-200000000−i2i2−i2i2i2−i2i2−i20000000000i2−i2−i2i2
χ534444-4-4-4-44-4-44400004-4-400000000-4400000000000000000000000000000000000000000
χ544444-4-4-4-4-44-4440000-44-4000000004-400000000000000000000000000000000000000000
χ5544-4-444-4-4-440004i4i−4i−4i4-4000−4i4i00000000000000000000000000000000000000000000000
χ5644-4-444-4-4-44000−4i−4i4i4i4-40004i−4i00000000000000000000000000000000000000000000000
χ5744-4-4-4-444440000000-4-4000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5844-4-4-4-444440000000-4-400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ5944-4-4-4-444-4-4000000044000000000000000000000022−22−222200000000000000000000000000
χ6044-4-4-4-444-4-40000000440000000000000000000000−222222−2200000000000000000000000000
χ614-44-44-44-4000004i−4i−4i4i000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ624-44-44-44-4000004i−4i−4i4i00000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ634-44-44-44-400000−4i4i4i−4i000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ644-44-44-44-400000−4i4i4i−4i00000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ654-4-444-4-4400-4-444-44-4004-440000000000000000000000000000000000000000000000000
χ664-4-444-4-4400-4-44-44-440044-40000000000000000000000000000000000000000000000000
χ674-4-44-444-4004-44000000-400004i−4i−4i4i0000000000000000000000000000000000000000000
χ684-4-44-444-4004-44000000-40000−4i4i4i−4i0000000000000000000000000000000000000000000
χ694-4-44-444-400-44-40000004000000000000000004-400000000000000000000000000000000
χ704-4-44-444-400-44-4000000400000000000000000-4400000000000000000000000000000000
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).