Finite Group Databasebeta

← Group #275608

Character table — Group #275608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444444888888888888888888888881616161616161616161616163232
order12222222444444442244444488884444488888888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111-1-1
χ311111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-111
χ7111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111111111-1-1
χ91111111111111111-1-1-1-1-1-1111111-11111-1-111-1-111111111-1-1-1-1-111-1-1-111-1-1-1-1-11
χ101111111111111111-1-1-1-1-1-1111111-11111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-111111-1-1111-1
χ121111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-11
χ131111111111111111-1-1-1-1-1-111-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-111111-1
χ141111111111111111-1-1-1-1-1-111-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11-1-1111-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-111-1-1-1-11-1
χ17222222222-2-222-2-222222-2-2-2-20000-222-2-2000000000000000000-20020000000000
χ18222222222-2-222-2-222222-2-2-2-20000-2-2-222000000000000000000200-20000000000
χ19222222222-2-222-2-22-2-2-2-222-2-20000222-2-2000000000000000000200-20000000000
χ20222222222-2-222-2-22-2-2-2-222-2-200002-2-222000000000000000000-20020000000000
χ2122222222-222-2-222-222-2-222-2-22222-2000022-2-2-2-200000000000000000000000000
χ2222222222-222-2-222-222-2-222-2-2-2-2-2-2-20000-2-2222200000000000000000000000000
χ2322222222-222-2-222-2-2-222-2-2-2-2222220000-2-2-2-22200000000000000000000000000
χ2422222222-222-2-222-2-2-222-2-2-2-2-2-2-2-2200002222-2-200000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2220000200000000002i2i−2i−2i0000000000000000002i−2i00
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-222000020000000000−2i−2i2i2i000000000000000000−2i2i00
χ2722222222-2-2-2-2-2-2-2-2-2-22222220000-200000000002i2i−2i−2i000000000000000000−2i2i00
χ2822222222-2-2-2-2-2-2-2-2-2-22222220000-20000000000−2i−2i2i2i0000000000000000002i−2i00
χ292222-2-2-2-202200-2-202-2002-20022-2-2000002-20000000022−2−222−2−20000002−22−20000
χ302222-2-2-2-202200-2-202-2002-20022-2-2000002-200000000−2−222−2−222000000−22−220000
χ312222-2-2-2-202200-2-202-2002-200-2-22200000-220000000022−2−222−2−2000000−22−220000
χ322222-2-2-2-202200-2-202-2002-200-2-22200000-2200000000−2−222−2−2220000002−22−20000
χ332222-2-2-2-202200-2-20-2200-220022-2-200000-220000000022−2−2−2−2220000002−2−220000
χ342222-2-2-2-202200-2-20-2200-220022-2-200000-2200000000−2−22222−2−2000000−222−20000
χ352222-2-2-2-202200-2-20-2200-2200-2-222000002-20000000022−2−2−2−222000000−222−20000
χ362222-2-2-2-202200-2-20-2200-2200-2-222000002-200000000−2−22222−2−20000002−2−220000
χ372-2-2222-2-2-22-22-22-220000002-2000002i−2i2i−2i00000000002-22-2000002i−2i00000000000
χ382-2-2222-2-2-22-22-22-220000002-2000002i−2i2i−2i0000000000-22-2200000−2i2i00000000000
χ392-2-2222-2-2-22-22-22-220000002-200000−2i2i−2i2i00000000002-22-200000−2i2i00000000000
χ402-2-2222-2-2-22-22-22-220000002-200000−2i2i−2i2i0000000000-22-22000002i−2i00000000000
χ412-2-2222-2-2-2-222-2-222000000-22000002i−2i−2i2i000000000000002-22-200002i−2i00000000
χ422-2-2222-2-2-2-222-2-222000000-22000002i−2i−2i2i00000000000000-22-220000−2i2i00000000
χ432-2-2222-2-2-2-222-2-222000000-2200000−2i2i2i−2i000000000000002-22-20000−2i2i00000000
χ442-2-2222-2-2-2-222-2-222000000-2200000−2i2i2i−2i00000000000000-22-2200002i−2i00000000
χ454444-4-4-4-40-4-4004404-400-440000000000000000000000000000000000000000000
χ464444-4-4-4-40-4-400440-44004-40000000000000000000000000000000000000000000
χ4744-4-44-44-44004-400-40000000000000000000000022−2222−220000000000000000000000
χ4844-4-44-44-44004-400-400000000000000000000000−2222−22220000000000000000000000
χ4944-4-44-44-4-400-44004000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5044-4-44-44-4-400-4400400000000000000000000000−2i22i22i2−2i20000000000000000000000
χ514-44-44-4-44400-4-4004000000002i2−2i22i2−2i200000002i2−2i20000000000000000000000000000
χ524-44-44-4-44400-4-400400000000−2i22i2−2i22i20000000−2i22i20000000000000000000000000000
χ534-44-44-4-44-4004400-4000000002i2−2i22i2−2i20000000−2i22i20000000000000000000000000000
χ544-44-44-4-44-4004400-400000000−2i22i2−2i22i200000002i2−2i20000000000000000000000000000
χ554-44-4-444-400000000004i−4i00002i2−2i2−2i22i200000000022−2200000000000000000000000000
χ564-44-4-444-400000000004i−4i0000−2i22i22i2−2i2000000000−222200000000000000000000000000
χ574-44-4-444-40000000000−4i4i00002i2−2i2−2i22i2000000000−222200000000000000000000000000
χ584-44-4-444-40000000000−4i4i0000−2i22i22i2−2i200000000022−2200000000000000000000000000
χ594-4-4444-4-444-4-444-4-4000000-4400000000000000000000000000000000000000000
χ604-4-4444-4-44-44-44-44-40000004-400000000000000000000000000000000000000000
χ614-4-44-4-44404-400-44000000000000000000000000000022−22−2222000000000000000000
χ624-4-44-4-44404-400-440000000000000000000000000000−222222−22000000000000000000
χ634-4-44-4-4440-44004-40000000000000000000000000000000022−22−222200000000000000
χ644-4-44-4-4440-44004-400000000000000000000000000000000−222222−2200000000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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