Finite Group Databasebeta

← Group #274451

Character table — Group #274451

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444444888888888888888888888881616161616161616161616163232
order12222222444444442244444488884444488888888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ41111111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1
χ91111111111111111-1-1-1-111-1-111111111-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111-1
χ101111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-11
χ111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-11
χ121111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-11-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-11111-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-11111-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-111-1-11111-1-1-1-11-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-111-11
χ17222222222-2-222-2-2222-2-2-2-2-2-2000022-2-22000000000000000000-22000000000000
χ18222222222-2-222-2-2222-2-2-2-2-2-20000-2-22220000000000000000002-2000000000000
χ19222222222-2-222-2-22-2-222-2-222000022-2-2-20000000000000000002-2000000000000
χ20222222222-2-222-2-22-2-222-2-2220000-2-222-2000000000000000000-22000000000000
χ2122222222-222-2-222-22222-2-2-2-222220000-2220000-2-2-2-20000000000000000000000
χ2222222222-222-2-222-22222-2-2-2-2-2-2-2-20000-2-2-2000022220000000000000000000000
χ2322222222-222-2-222-2-2-2-2-2-2-222222200002-2-20000-2-2220000000000000000000000
χ2422222222-222-2-222-2-2-2-2-2-2-222-2-2-2-20000222000022-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2222200000000-200000000002i2i−2i−2i0000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-222-2-2222200000000-20000000000−2i−2i2i2i000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-200000000200000000002i2i−2i−2i000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-20000000020000000000−2i−2i2i2i0000000000002i−2i0000
χ292222-2-2-2-202200-2-202-22-2000022-2-2000002-222−2−20000000022−2−20000002−2002−200
χ302222-2-2-2-202200-2-202-22-2000022-2-2000002-2−2−22200000000−2−222000000−2200−2200
χ312222-2-2-2-202200-2-202-22-20000-2-22200000-2222−2−20000000022−2−2000000−2200−2200
χ322222-2-2-2-202200-2-202-22-20000-2-22200000-22−2−22200000000−2−2220000002−2002−200
χ332222-2-2-2-202200-2-20-22-22000022-2-200000-2222−2−200000000−2−222000000−22002−200
χ342222-2-2-2-202200-2-20-22-22000022-2-200000-22−2−2220000000022−2−20000002−200−2200
χ352222-2-2-2-202200-2-20-22-220000-2-222000002-222−2−200000000−2−2220000002−200−2200
χ362222-2-2-2-202200-2-20-22-220000-2-222000002-2−2−2220000000022−2−2000000−22002−200
χ372-2-22-22-2222-22-22-2-200002-20000002i−2i2i−2i0002i−2i2i−2i000000000000002-20000000000
χ382-2-22-22-2222-22-22-2-200002-20000002i−2i2i−2i000−2i2i−2i2i00000000000000-220000000000
χ392-2-22-22-2222-22-22-2-200002-2000000−2i2i−2i2i0002i−2i2i−2i00000000000000-220000000000
χ402-2-22-22-2222-22-22-2-200002-2000000−2i2i−2i2i000−2i2i−2i2i000000000000002-20000000000
χ412-2-22-22-222-222-2-22-20000-220000002i−2i−2i2i0000000000000002i−2i2i−2i00002-200000000
χ422-2-22-22-222-222-2-22-20000-220000002i−2i−2i2i000000000000000−2i2i−2i2i0000-2200000000
χ432-2-22-22-222-222-2-22-20000-22000000−2i2i2i−2i0000000000000002i−2i2i−2i0000-2200000000
χ442-2-22-22-222-222-2-22-20000-22000000−2i2i2i−2i000000000000000−2i2i−2i2i00002-200000000
χ454444-4-4-4-40-4-4004404-4-44000000000000000000000000000000000000000000000
χ464444-4-4-4-40-4-400440-444-4000000000000000000000000000000000000000000000
χ4744-4-44-4-44400-4-4004000000002i2−2i22i2−2i2000000000002i2−2i2000000000000000000000000
χ4844-4-44-4-44400-4-400400000000−2i22i2−2i22i200000000000−2i22i2000000000000000000000000
χ4944-4-44-4-44-4004400-4000000002i2−2i22i2−2i200000000000−2i22i2000000000000000000000000
χ5044-4-44-4-44-4004400-400000000−2i22i2−2i22i2000000000002i2−2i2000000000000000000000000
χ5144-4-4-444-4000000000000004-42i2−2i2−2i22i200000000000002i2−2i20000000000000000000000
χ5244-4-4-444-4000000000000004-4−2i22i22i2−2i20000000000000−2i22i20000000000000000000000
χ5344-4-4-444-400000000000000-442i2−2i2−2i22i20000000000000−2i22i20000000000000000000000
χ5444-4-4-444-400000000000000-44−2i22i22i2−2i200000000000002i2−2i20000000000000000000000
χ554-44-4-4-444400-4400-40000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ564-44-4-4-444400-4400-4000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ574-44-4-4-444-4004-400400000000000000000000000000022−22−2222000000000000000000
χ584-44-4-4-444-4004-4004000000000000000000000000000−222222−22000000000000000000
χ594-4-444-44-404-400-44000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ604-4-444-44-404-400-4400000000000000000000−2i22i22i2−2i200000000000000000000000000
χ614-4-444-44-40-44004-4000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ624-4-444-44-40-44004-400000000000000000000000000000000−2i22i22i2−2i200000000000000
χ634-4-44-44-44-44-4-444-440000-440000000000000000000000000000000000000000000
χ644-4-44-44-44-4-44-44-44400004-40000000000000000000000000000000000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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