Finite Group Databasebeta

← Group #317686

Character table — Group #317686

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ91111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1
χ121111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-111
χ131111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-111
χ141111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-11111-1-111-1-1
χ151111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-11111-1-1-1-111
χ161111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ1722222222222222-2-2-222-2-2-222-2-2-2-20000000000000000000000002-22-2000000000000
χ1822222222222222-2-2-222-2-2-222-2-2-2-2000000000000000000000000-22-22000000000000
χ192222222222-2-2-2-2-2-2-222-2-2-2-2-222220000000000000000000000002-2-22000000000000
χ202222222222-2-2-2-2-2-2-222-2-2-2-2-22222000000000000000000000000-222-2000000000000
χ2122222222-2-22222222-2-22-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000
χ2222222222-2-22222222-2-22-2-2-2-222-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-222-2-2-2-2220000000000000000000000000000000000002i−2i2i−2i
χ2422222222-2-22222-2-2-2-2-2-222-2-2-2-222000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-2-2-2-2-2222-2-22-2-222-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-22-2-222-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000−2i2i2i−2i
χ292222-2-2-2-20022-2-22-2-200200002-200000022-2-2000022-2-2000000000000i2−i2i2−i2i2−i2i2−i20000
χ302222-2-2-2-20022-2-22-2-200200002-200000022-2-2000022-2-2000000000000−i2i2−i2i2−i2i2−i2i20000
χ312222-2-2-2-20022-2-22-2-200200002-2000000-2-2220000-2-222000000000000i2−i2i2−i2−i2i2−i2i20000
χ322222-2-2-2-20022-2-22-2-200200002-2000000-2-2220000-2-222000000000000−i2i2−i2i2i2−i2i2−i20000
χ332222-2-2-2-200-2-2222-2-20020000-2200000022-2-20000-2-222000000000000i2−i2−i2i2i2−i2−i2i20000
χ342222-2-2-2-200-2-2222-2-20020000-2200000022-2-20000-2-222000000000000−i2i2i2−i2−i2i2i2−i20000
χ352222-2-2-2-200-2-2222-2-20020000-22000000-2-222000022-2-2000000000000i2−i2−i2i2−i2i2i2−i20000
χ362222-2-2-2-200-2-2222-2-20020000-22000000-2-222000022-2-2000000000000−i2i2i2−i2i2−i2−i2i20000
χ3722-2-222-2-22-20000-22-22-222-20000002i2i−2i−2i2i−2i2i−2i00000000002i−2i002-20000000000000000
χ3822-2-222-2-22-20000-22-22-222-20000002i2i−2i−2i2i−2i2i−2i0000000000−2i2i00-220000000000000000
χ3922-2-222-2-22-20000-22-22-222-2000000−2i−2i2i2i−2i2i−2i2i00000000002i−2i00-220000000000000000
χ4022-2-222-2-22-20000-22-22-222-2000000−2i−2i2i2i−2i2i−2i2i0000000000−2i2i002-20000000000000000
χ4122-2-222-2-2-220000-22-2-222-220000002i2i−2i−2i−2i2i−2i2i000000002-2002i−2i000000000000000000
χ4222-2-222-2-2-220000-22-2-222-220000002i2i−2i−2i−2i2i−2i2i00000000-2200−2i2i000000000000000000
χ4322-2-222-2-2-220000-22-2-222-22000000−2i−2i2i2i2i−2i2i−2i000000002-200−2i2i000000000000000000
χ4422-2-222-2-2-220000-22-2-222-22000000−2i−2i2i2i2i−2i2i−2i00000000-22002i−2i000000000000000000
χ454444-4-4-4-40044-4-4-44400-40000-44000000000000000000000000000000000000000000
χ464444-4-4-4-400-4-444-44400-400004-4000000000000000000000000000000000000000000
χ4744-4-444-4-44-400004-444-4-4-440000000000000000000000000000000000000000000000
χ4844-4-444-4-4-4400004-44-44-44-40000000000000000000000000000000000000000000000
χ4944-4-4-4-44400000044-400-4000000000000000044-4-40000000000000000000000000000
χ5044-4-4-4-44400000044-400-40000000000000000-4-4440000000000000000000000000000
χ5144-4-4-4-444000000-4-440040000000000004i−4i−4i4i00000000000000000000000000000000
χ5244-4-4-4-444000000-4-44004000000000000−4i4i4i−4i00000000000000000000000000000000
χ534-44-44-44-40000000000000000004i−4i22−2222−22000000002i2−2i22i2−2i2000000000000000000000000
χ544-44-44-44-40000000000000000004i−4i−2222−222200000000−2i22i2−2i22i2000000000000000000000000
χ554-44-44-44-4000000000000000000−4i4i22−2222−2200000000−2i22i2−2i22i2000000000000000000000000
χ564-44-44-44-4000000000000000000−4i4i−2222−2222000000002i2−2i22i2−2i2000000000000000000000000
χ574-44-4-44-444-40000000-44000000000000000002i2−2i22i2−2i22i2−2i2−2i22i2000000000000000000000000
χ584-44-4-44-444-40000000-4400000000000000000−2i22i2−2i22i2−2i22i22i2−2i2000000000000000000000000
χ594-44-4-44-44-4400000004-4000000000000000002i2−2i22i2−2i2−2i22i22i2−2i2000000000000000000000000
χ604-44-4-44-44-4400000004-400000000000000000−2i22i2−2i22i22i2−2i2−2i22i2000000000000000000000000
χ614-4-444-4-44004-44-4000000000000002i2−2i2−2i22i200002i2−2i2−2i22i20000000000000000000000000000
χ624-4-444-4-44004-44-400000000000000−2i22i22i2−2i20000−2i22i22i2−2i20000000000000000000000000000
χ634-4-444-4-4400-44-44000000000000002i2−2i2−2i22i20000−2i22i22i2−2i20000000000000000000000000000
χ644-4-444-4-4400-44-4400000000000000−2i22i22i2−2i200002i2−2i2−2i22i20000000000000000000000000000
χ654-4-44-444-4444-4-44000-4-40004-400000000000000000000000000000000000000000000
χ664-4-44-444-444-444-4000-4-4000-4400000000000000000000000000000000000000000000
χ674-4-44-444-4-4-44-4-4400044000-4400000000000000000000000000000000000000000000
χ684-4-44-444-4-4-4-444-4000440004-400000000000000000000000000000000000000000000

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