Finite Group Databasebeta

← Group #259039

Character table — Group #259039

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444448888888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444488888888222244444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-111-1-1111111-1-111-1-11111-1-1-1-1-1-1111-11-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-111
χ111111111111111111-1-1-1-111-1-11111-1-111-1-1111111-1-1-1-1-1-111-11-11-1-1-1-111-1-111
χ121111111111111111-1-1-1-111-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-11-111111-1-111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11-1-111111-1-1-1-111
χ141111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111-1-11-1-1-1-11111-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-111-111-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-111-1-1-111-1-1-1-111
χ172222222222-2-2-222-222-2-2-2-22-200000000222200000000000000-2-20000000000
χ182222222222-2-2-222-222-2-2-2-22-200000000-2-2-2-200000000000000220000000000
χ192222222222-2-2-222-2-2-222-2-2-220000000022-2-200000000000000-220000000000
χ202222222222-2-2-222-2-2-222-2-2-2200000000-2-222000000000000002-20000000000
χ2122222222-2-2222-2-222222-2-2-2-2000022220000000000000000-2-2000000000000
χ2222222222-2-2222-2-222222-2-2-2-20000-2-2-2-2000000000000000022000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-222000022-2-20000000000000000-22000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2220000-2-22200000000000000002-2000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2222-2-200000000000000002-20000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-22-2-2220000000000000000-220000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222-222-2-20000000000000000-220000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222-2-2-22200000000000000002-20000000000000000
χ292222-2-2-2-2222-2-2-2-2200002-2002i−2i2i−2i000000002i2i−2i−2i0000002-200000000000000
χ302222-2-2-2-2222-2-2-2-2200002-2002i−2i2i−2i00000000−2i−2i2i2i000000-2200000000000000
χ312222-2-2-2-2222-2-2-2-2200002-200−2i2i−2i2i000000002i2i−2i−2i000000-2200000000000000
χ322222-2-2-2-2222-2-2-2-2200002-200−2i2i−2i2i00000000−2i−2i2i2i0000002-200000000000000
χ332222-2-2-2-2-2-2-22222-200002-2002i−2i−2i2i00000000000022-2-2000000002i−2i00000000
χ342222-2-2-2-2-2-2-22222-200002-2002i−2i−2i2i000000000000-2-22200000000−2i2i00000000
χ352222-2-2-2-2-2-2-22222-200002-200−2i2i2i−2i00000000000022-2-200000000−2i2i00000000
χ362222-2-2-2-2-2-2-22222-200002-200−2i2i2i−2i000000000000-2-222000000002i−2i00000000
χ372-22-222-2-20022-200-22-22-2000000002i−2i2i−2i00002−22−22−22−20000000000i2−i2i2−i20000
χ382-22-222-2-20022-200-22-22-2000000002i−2i2i−2i0000−22−22−22−220000000000−i2i2−i2i20000
χ392-22-222-2-20022-200-22-22-200000000−2i2i−2i2i00002−22−22−22−20000000000−i2i2−i2i20000
χ402-22-222-2-20022-200-22-22-200000000−2i2i−2i2i0000−22−22−22−220000000000i2−i2i2−i20000
χ412-22-222-2-20022-200-2-22-22000000002i−2i−2i2i00002−22−2−22−220000000000i2−i2−i2i20000
χ422-22-222-2-20022-200-2-22-22000000002i−2i−2i2i0000−22−222−22−20000000000−i2i2i2−i20000
χ432-22-222-2-20022-200-2-22-2200000000−2i2i2i−2i00002−22−2−22−220000000000−i2i2i2−i20000
χ442-22-222-2-20022-200-2-22-2200000000−2i2i2i−2i0000−22−222−22−20000000000i2−i2−i2i20000
χ454444-4-4-4-444-444-4-4-40000-440000000000000000000000000000000000000000
χ464444-4-4-4-4-4-44-4-44440000-440000000000000000000000000000000000000000
χ4744-4-44-44-44-40004-400000000000000000004i−4i00000000000000000000000000
χ4844-4-44-44-44-40004-40000000000000000000−4i4i00000000000000000000000000
χ4944-4-44-44-4-44000-44000000000000000004i−4i0000000000000000000000000000
χ5044-4-44-44-4-44000-4400000000000000000−4i4i0000000000000000000000000000
χ5144-4-4-44-444-4000-440000000000000000000000000000000000000000000002i2−2i2
χ5244-4-4-44-444-4000-44000000000000000000000000000000000000000000000−2i22i2
χ5344-4-4-44-44-440004-400000000000000000000000000000000000000000002i2−2i200
χ5444-4-4-44-44-440004-40000000000000000000000000000000000000000000−2i22i200
χ554-44-444-4-400-4-440044-4-44000000000000000000000000000000000000000000
χ564-44-444-4-400-4-44004-444-4000000000000000000000000000000000000000000
χ574-44-4-4-444004-4400-4000000000000000000002i2−2i2−2i22i20000000000000000000000
χ584-44-4-4-444004-4400-400000000000000000000−2i22i22i2−2i20000000000000000000000
χ594-44-4-4-44400-44-400400000000000000000000000022−22−2222000000000000000000
χ604-44-4-4-44400-44-4004000000000000000000000000−222222−22000000000000000000
χ618-8-888-8-88000000000000000000000000000000000000000000000000000000
χ628-8-88-888-8000000000000000000000000000000000000000000000000000000

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