Finite Group Databasebeta

← Group #287539

Character table — Group #287539

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444444888888888888888888888881616161616161616161616163232
order12222222444444444444444488884444488888888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111111111-1-1-1-11-1-11-1-111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1
χ7111111111111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-111-11111-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ91111111111111111-1-1-1-111-1-11111-11111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111-1
χ101111111111111111-1-1-1-111-1-11111-11111-1-1-1-1-1-111-1-111111111-111-1-1-1-1-111-1-1-11
χ111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ121111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-11111111-1-11-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-111-1-1-11111-1-11-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-11-1-1111-1-111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1111-1
χ17222222222-222-2-22-22222-2-2-2-22222-20000220000-2-2-2-20000000000000000000000
χ18222222222-222-2-22-22222-2-2-2-2-2-2-2-2-20000-2-2000022220000000000000000000000
χ19222222222-222-2-22-2-2-2-2-2-2-222222220000-2-20000-2-2220000000000000000000000
χ20222222222-222-2-22-2-2-2-2-2-2-222-2-2-2-22000022000022-2-20000000000000000000000
χ2122222222-22-2-222-2222-2-2-2-2220000-222-2-2000000000000000000200-20000000000
χ2222222222-22-2-222-2222-2-2-2-2220000-2-2-222000000000000000000-20020000000000
χ2322222222-22-2-222-22-2-222-2-2-2-20000222-2-2000000000000000000-20020000000000
χ2422222222-22-2-222-22-2-222-2-2-2-200002-2-222000000000000000000200-20000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2-200002000000000000002i2i−2i−2i00000000002i−2i000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-2-20000200000000000000−2i−2i2i2i0000000000−2i2i000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222220000-2000000000000002i2i−2i−2i0000000000−2i2i000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222220000-200000000000000−2i−2i2i2i00000000002i−2i000000
χ292222-2-2-2-2202-200-202-22-2000022-2-2000002-222−2−20000000022−2−2000000002−22−200
χ302222-2-2-2-2202-200-202-22-2000022-2-2000002-2−2−22200000000−2−22200000000−22−2200
χ312222-2-2-2-2202-200-202-22-20000-2-22200000-2222−2−20000000022−2−200000000−22−2200
χ322222-2-2-2-2202-200-202-22-20000-2-22200000-22−2−22200000000−2−222000000002−22−200
χ332222-2-2-2-2202-200-20-22-22000022-2-200000-2222−2−200000000−2−22200000000−222−200
χ342222-2-2-2-2202-200-20-22-22000022-2-200000-22−2−2220000000022−2−2000000002−2−2200
χ352222-2-2-2-2202-200-20-22-220000-2-222000002-222−2−200000000−2−222000000002−2−2200
χ362222-2-2-2-2202-200-20-22-220000-2-222000002-2−2−2220000000022−2−200000000−222−200
χ3722-2-22-22-22-2-222-2-2200002-200000000000002i−2i2i−2i00002i−2i2i−2i000000002-200000000
χ3822-2-22-22-22-2-222-2-2200002-200000000000002i−2i2i−2i0000−2i2i−2i2i00000000-2200000000
χ3922-2-22-22-22-2-222-2-2200002-20000000000000−2i2i−2i2i00002i−2i2i−2i00000000-2200000000
χ4022-2-22-22-22-2-222-2-2200002-20000000000000−2i2i−2i2i0000−2i2i−2i2i000000002-200000000
χ4122-2-22-22-2-222-2-222-200002-20000000000000000000002-2-222i−2i2i−2i02i−2i00000000000
χ4222-2-22-22-2-222-2-222-200002-20000000000000000000002-2-22−2i2i−2i2i0−2i2i00000000000
χ4322-2-22-22-2-222-2-222-200002-2000000000000000000000-222-22i−2i2i−2i0−2i2i00000000000
χ4422-2-22-22-2-222-2-222-200002-2000000000000000000000-222-2−2i2i−2i2i02i−2i00000000000
χ454444-4-4-4-4-40-4400404-4-44000000000000000000000000000000000000000000000
χ464444-4-4-4-4-40-440040-444-4000000000000000000000000000000000000000000000
χ4744-4-44-44-444-44-44-4-40000-440000000000000000000000000000000000000000000
χ4844-4-44-44-4-4-44-44-4440000-440000000000000000000000000000000000000000000
χ4944-4-4-44-4440-4-4004000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ5044-4-4-44-4440-4-400400000000000000000000−2i22i22i2−2i200000000000000000000000000
χ5144-4-4-44-44-404400-4000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ5244-4-4-44-44-404400-400000000000000000000000000000000−2i22i22i2−2i200000000000000
χ534-44-44-4-44000000000000004-42i2−2i22i2−2i200000000000002i2−2i20000000000000000000000
χ544-44-44-4-44000000000000004-4−2i22i2−2i22i20000000000000−2i22i20000000000000000000000
χ554-44-44-4-4400000000000000-442i2−2i22i2−2i20000000000000−2i22i20000000000000000000000
χ564-44-44-4-4400000000000000-44−2i22i2−2i22i200000000000002i2−2i20000000000000000000000
χ574-44-4-444-40400-4-404000000002i2−2i2−2i22i2000000000002i2−2i2000000000000000000000000
χ584-44-4-444-40400-4-40400000000−2i22i22i2−2i200000000000−2i22i2000000000000000000000000
χ594-44-4-444-40-400440-4000000002i2−2i2−2i22i200000000000−2i22i2000000000000000000000000
χ604-44-4-444-40-400440-400000000−2i22i22i2−2i2000000000002i2−2i2000000000000000000000000
χ614-4-44-4-44404004-40-400000000000004i−4i0000000000000000000000000000000000
χ624-4-44-4-44404004-40-40000000000000−4i4i0000000000000000000000000000000000
χ634-4-44-4-4440-400-44040000000000000004-400000000000000000000000000000000
χ644-4-44-4-4440-400-4404000000000000000-4400000000000000000000000000000000
χ658-8-8888-8-8000000000000000000000000000000000000000000000000000000000

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