Finite Group Databasebeta

← Group #258721

Character table — Group #258721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422444444488888888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-1111-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111
χ5111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-11-1-111111-1-1-1111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-111-1-1
χ101111111111111111-1-1-1-11-1-111111-1-1-111-1-1-1-11111-1-1-1-11111-11-1-1-1-1-1-11111-1-111
χ111111111111111111-1-1-1-11-1-1111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1111-1-1-1-111-1-111
χ121111111111111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111111-1-1-1-111-1-1
χ131111111111111111-1-1-1-11-1-11-1-111-111111111-1-1-1-1-1-1-1-11111-1-11-11111-1-1-1-1-1-111
χ141111111111111111-1-1-1-11-1-11-1-111-11111-1-1-1-111111111-1-1-1-1-1-11-111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-11-1-11-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-11-1-11-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-111-1-11111-1-1-1-111
χ172222222222-2-222-2-22222-2-2-2-20022-200-2-20000000000000000-2002000000000000
χ182222222222-2-222-2-22222-2-2-2-200-2-2-200220000000000000000200-2000000000000
χ192222222222-2-222-2-2-2-2-2-2-222-20022200-2-20000000000000000200-2000000000000
χ202222222222-2-222-2-2-2-2-2-2-222-200-2-2200220000000000000000-2002000000000000
χ2122222222-2-222-2-22222-2-2-222-22200-2220000000000000000000-2-20000000000000
χ2222222222-2-222-2-22222-2-2-222-2-2-200-2-2-20000000000000000000220000000000000
χ2322222222-2-222-2-222-2-222-2-2-2-222002-2-20000000000000000000-220000000000000
χ2422222222-2-222-2-222-2-222-2-2-2-2-2-20022200000000000000000002-20000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-22-2-22000020000000000000000000000002-2002-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-22-2-2200002000000000000000000000000-2200-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222220000-20000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222220000-2000000000000000000000000-22002-2000000
χ2922-22-2-22-22-2222-2-2-20000-2002002i−2i0002i−2i22-2-20000000000000000002i−2i00000000
χ3022-22-2-22-22-2222-2-2-20000-2002002i−2i0002i−2i-2-222000000000000000000−2i2i00000000
χ3122-22-2-22-22-2222-2-2-20000-200200−2i2i000−2i2i22-2-2000000000000000000−2i2i00000000
χ3222-22-2-22-22-2222-2-2-20000-200200−2i2i000−2i2i-2-2220000000000000000002i−2i00000000
χ3322-22-2-22-22-2-2-22-2220000200-2002i−2i000−2i2i00002i2i−2i−2i0000000000000000002-20000
χ3422-22-2-22-22-2-2-22-2220000200-2002i−2i000−2i2i0000−2i−2i2i2i000000000000000000-220000
χ3522-22-2-22-22-2-2-22-2220000200-200−2i2i0002i−2i00002i2i−2i−2i000000000000000000-220000
χ3622-22-2-22-22-2-2-22-2220000200-200−2i2i0002i−2i0000−2i−2i2i2i0000000000000000002-20000
χ372-2-2222-2-2002-2002-22i−2i0002i−2i02-20002i−2i00i2−i2i2−i22−22−2i2i2−i2−i222−2−20000000000000000
χ382-2-2222-2-2002-2002-22i−2i0002i−2i02-20002i−2i00−i2i2−i2i2−22−22−i2−i2i2i2−2−2220000000000000000
χ392-2-2222-2-2002-2002-22i−2i0002i−2i0-22000−2i2i00i2−i2i2−i22−22−2−i2−i2i2i2−2−2220000000000000000
χ402-2-2222-2-2002-2002-22i−2i0002i−2i0-22000−2i2i00−i2i2−i2i2−22−22i2i2−i2−i222−2−20000000000000000
χ412-2-2222-2-2002-2002-2−2i2i000−2i2i02-2000−2i2i00i2−i2i2−i2−22−22i2i2−i2−i2−2−2220000000000000000
χ422-2-2222-2-2002-2002-2−2i2i000−2i2i02-2000−2i2i00−i2i2−i2i22−22−2−i2−i2i2i222−2−20000000000000000
χ432-2-2222-2-2002-2002-2−2i2i000−2i2i0-220002i−2i00i2−i2i2−i2−22−22−i2−i2i2i222−2−20000000000000000
χ442-2-2222-2-2002-2002-2−2i2i000−2i2i0-220002i−2i00−i2i2−i2i22−22−2i2i2−i2−i2−2−2220000000000000000
χ45444-44-4-4-44400-4-40000000000000000000000000000000000000000000000022−2200
χ46444-44-4-4-44400-4-400000000000000000000000000000000000000000000000−222200
χ47444-44-4-4-4-4-4004400000000000000000000000000000000000000000000000002i2−2i2
χ48444-44-4-4-4-4-400440000000000000000000000000000000000000000000000000−2i22i2
χ4944-44-4-44-4-4444-44-4-40000400-400000000000000000000000000000000000000000
χ5044-44-4-44-4-44-4-4-44440000-400400000000000000000000000000000000000000000
χ5144-4-4-44-444-400-440000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ5244-4-4-44-444-400-44000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ5344-4-4-44-44-44004-400000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ5444-4-4-44-44-44004-40000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ554-444-4-4-44004-400-44000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ564-444-4-4-44004-400-4400000000000000000−2i22i22i2−2i20000000000000000000000000000
χ574-444-4-4-4400-44004-40000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ584-444-4-4-4400-44004-4000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ594-44-4-444-400000000004i−4i0000000000000000000002-2-222i−2i−2i2i0000000000000000
χ604-44-4-444-400000000004i−4i000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ614-44-4-444-40000000000−4i4i0000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ624-44-4-444-40000000000−4i4i000000000000000000000-222-22i−2i−2i2i0000000000000000
χ634-4-4444-4-400-4400-444i−4i000−4i4i000000000000000000000000000000000000000000
χ644-4-4444-4-400-4400-44−4i4i0004i−4i000000000000000000000000000000000000000000
χ658-8-8-88-888000000000000000000000000000000000000000000000000000000000

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