Finite Group Databasebeta

← Group #120013

Character table — Group #120013

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222222222222222222222444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111111-1-111-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-111-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-222-2-2-2-222220000-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-222-2-2-2-2-2-2-2-200002222000000000000000000000000
χ192222222222-2-222-2-2-2-2-2-2-2-2222222-2-20000-2-222000000000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-22222-2-222000022-2-2000000000000000000000000
χ2122222222-2-222-2-22222-2-2-2-22-22-20000000000000000000000002-22-200000000
χ2222222222-2-222-2-22222-2-2-2-22-22-2000000000000000000000000-22-2200000000
χ2322222222-2-222-2-222-2-222-2-2-22-22000000000000000000002-22-2000000000000
χ2422222222-2-222-2-222-2-222-2-2-22-2200000000000000000000-22-22000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-22-220000000000000000000000002i−2i−2i2i00000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-22-22000000000000000000000000−2i2i2i−2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222-22-2000000000000000000002i−2i−2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222-22-200000000000000000000−2i2i2i−2i000000000000
χ292222-2-2-2-22222-2-2-2-22-22-22-22-2-2200000000000000000000000000002-22-20000
χ302222-2-2-2-22222-2-2-2-22-22-22-22-2-220000000000000000000000000000-22-220000
χ312222-2-2-2-22222-2-2-2-2-22-222-2-222-2000000000000000000000000000000002-22-2
χ322222-2-2-2-22222-2-2-2-2-22-222-2-222-200000000000000000000000000000000-22-22
χ332222-2-2-2-222-2-2-2-2222-22-2-22-222-200000000000000000000000000002i−2i−2i2i0000
χ342222-2-2-2-222-2-2-2-2222-22-2-22-222-20000000000000000000000000000−2i2i2i−2i0000
χ352222-2-2-2-222-2-2-2-222-22-22-222-2-22000000000000000000000000000000002i−2i−2i2i
χ362222-2-2-2-222-2-2-2-222-22-22-222-2-2200000000000000000000000000000000−2i2i2i−2i
χ372222-2-2-2-2-2-22222-2-22-2-22-2222-2-200000000000000002-22-20000000000000000
χ382222-2-2-2-2-2-22222-2-22-2-22-2222-2-20000000000000000-22-220000000000000000
χ392222-2-2-2-2-2-22222-2-2-222-2-22-2-22200002i2i−2i−2i00002i2i−2i−2i00000000000000000000
χ402222-2-2-2-2-2-22222-2-2-222-2-22-2-2220000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000
χ412222-2-2-2-2-2-2-2-222222-2-222-2-2-22200000000000000002-2-220000000000000000
χ422222-2-2-2-2-2-2-2-222222-2-222-2-2-2220000000000000000-222-20000000000000000
χ432222-2-2-2-2-2-2-2-22222-222-22-222-2-200002i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ442222-2-2-2-2-2-2-2-22222-222-22-222-2-20000−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ4544-4-444-4-4004-4004-4000000000000002i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ4644-4-444-4-4004-4004-400000000000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ4744-4-444-4-400-4400-44000000000000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000
χ4844-4-444-4-400-4400-4400000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ4944-4-4-4-444004-400-44000000000000002-2-2200002-2-2200000000000000000000
χ5044-4-4-4-444004-400-4400000000000000-222-20000-222-200000000000000000000
χ5144-4-4-4-44400-44004-4000000000000002-2-220000-222-200000000000000000000
χ5244-4-4-4-44400-44004-400000000000000-222-200002-2-2200000000000000000000
χ534-44-44-44-44-4004-4000000000000004i−4i00000000000000000000000000000000
χ544-44-44-44-44-4004-400000000000000−4i4i00000000000000000000000000000000
χ554-44-44-44-4-4400-440000000000004i−4i0000000000000000000000000000000000
χ564-44-44-44-4-4400-44000000000000−4i4i0000000000000000000000000000000000
χ574-44-4-44-444-400-44000000000000000000004-400000000000000000000000000
χ584-44-4-44-444-400-4400000000000000000000-4400000000000000000000000000
χ594-44-4-44-44-44004-400000000000000000000004-4000000000000000000000000
χ604-44-4-44-44-44004-40000000000000000000000-44000000000000000000000000
χ618-8-888-8-88000000000000000000000000000000000000000000000000000000
χ628-8-88-888-8000000000000000000000000000000000000000000000000000000

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