Finite Group Databasebeta

← Group #258733

Character table — Group #258733

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422444444488888888888888884444444444448888
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
χ311111111111111111111111111-1-1111-1-111111111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-111-1-1111111
χ5111111111111111111111111-1-111-1-111111111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-1-1-1
χ6111111111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-111111111-11-1-1-11-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111
χ8111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111111111111111-1-1-1-11-1-111111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-111-1-1
χ101111111111111111-1-1-1-11-1-111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-111
χ111111111111111111-1-1-1-11-1-1111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-1-1-111-1-111
χ121111111111111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11111111-1-1-1-111-1-1
χ131111111111111111-1-1-1-11-1-11-1-11111-1111111-1-1-1-1-1-1-1-111111-111-1-111-1-1-1-1-1-111
χ141111111111111111-1-1-1-11-1-11-1-11111-111-1-1-1-111111111-1-1-1-11-111-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-11-1-11-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-1-1111111-1-1
χ161111111111111111-1-1-1-11-1-11-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-111111-1-1-1-111
χ172222222222-2-222-2-222-2-2-222-2220022-2000000000000000000-2000-200000000000
χ182222222222-2-222-2-222-2-2-222-2-2-200-2-2-20000000000000000002000200000000000
χ192222222222-2-222-2-2-2-222-2-2-2-22200-2-220000000000000000002000-200000000000
χ202222222222-2-222-2-2-2-222-2-2-2-2-2-200222000000000000000000-2000200000000000
χ2122222222-2-222-2-2222222-2-2-2-2002200-2-2-2000000000000000002000-20000000000
χ2222222222-2-222-2-2222222-2-2-2-200-2-200-22200000000000000000-200020000000000
χ2322222222-2-222-2-222-2-2-2-2-222-20022002-2-200000000000000000-200020000000000
χ2422222222-2-222-2-222-2-2-2-2-222-200-2-200222000000000000000002000-20000000000
χ2522222222-2-2-2-2-2-2-2-222-2-22-2-220000002000000000000000000002-200002-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-22-2-22000000200000000000000000000-220000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222000000-2000000000000000000002-20000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222222000000-200000000000000000000-2200002-2000000
χ292-222-2-2-222-2002-2002i−2i0002i−2i02-2002i−2i000i2i2−i2−i222−2−2i2i2−i2−i222−2−20000000000000000
χ302-222-2-2-222-2002-2002i−2i0002i−2i02-2002i−2i000−i2−i2i2i2−2−222−i2−i2i2i2−2−2220000000000000000
χ312-222-2-2-222-2002-2002i−2i0002i−2i0-2200−2i2i000i2i2−i2−i222−2−2−i2−i2i2i2−2−2220000000000000000
χ322-222-2-2-222-2002-2002i−2i0002i−2i0-2200−2i2i000−i2−i2i2i2−2−222i2i2−i2−i222−2−20000000000000000
χ332-222-2-2-222-2002-200−2i2i000−2i2i02-200−2i2i000i2i2−i2−i2−2−222i2i2−i2−i2−2−2220000000000000000
χ342-222-2-2-222-2002-200−2i2i000−2i2i02-200−2i2i000−i2−i2i2i222−2−2−i2−i2i2i222−2−20000000000000000
χ352-222-2-2-222-2002-200−2i2i000−2i2i0-22002i−2i000i2i2−i2−i2−2−222−i2−i2i2i222−2−20000000000000000
χ362-222-2-2-222-2002-200−2i2i000−2i2i0-22002i−2i000−i2−i2i2i222−2−2i2i2−i2−i2−2−2220000000000000000
χ372-22-22-22-2222-2-2-22-20000-2002002i−2i0002i−2i00002-22-20000000000000000002i−2i0000
χ382-22-22-22-2222-2-2-22-20000-2002002i−2i0002i−2i0000-22-22000000000000000000−2i2i0000
χ392-22-22-22-2222-2-2-22-20000-200200−2i2i000−2i2i00002-22-2000000000000000000−2i2i0000
χ402-22-22-22-2222-2-2-22-20000-200200−2i2i000−2i2i0000-22-220000000000000000002i−2i0000
χ412-22-22-22-2-2-22-2222-20000200-2002i−2i000−2i2i2i−2i2i−2i0000000000000000002-200000000
χ422-22-22-22-2-2-22-2222-20000200-2002i−2i000−2i2i−2i2i−2i2i000000000000000000-2200000000
χ432-22-22-22-2-2-22-2222-20000200-200−2i2i0002i−2i2i−2i2i−2i000000000000000000-2200000000
χ442-22-22-22-2-2-22-2222-20000200-200−2i2i0002i−2i−2i2i−2i2i0000000000000000002-200000000
χ45444-4-44-4-44-400-440000000000000000000000022−22−2222000000000000000000000000
χ46444-4-44-4-44-400-4400000000000000000000000−222222−22000000000000000000000000
χ47444-4-44-4-4-44004-4000000000000000000022−22−22220000000000000000000000000000
χ48444-4-44-4-4-44004-40000000000000000000−222222−220000000000000000000000000000
χ4944-44-4-44-4004400-4-400000000000000000000000000000000000000000000022−2200
χ5044-44-4-44-4004400-4-4000000000000000000000000000000000000000000000−222200
χ5144-44-4-44-400-4-40044000000000000000000000000000000000000000000000002i2−2i2
χ5244-44-4-44-400-4-4004400000000000000000000000000000000000000000000000−2i22i2
χ5344-4-44-4-4400000000004i−4i0000000000000000000002i−2i2i−2i2-22-20000000000000000
χ5444-4-44-4-4400000000004i−4i000000000000000000000−2i2i−2i2i-22-220000000000000000
χ5544-4-44-4-440000000000−4i4i0000000000000000000002i−2i2i−2i-22-220000000000000000
χ5644-4-44-4-440000000000−4i4i000000000000000000000−2i2i−2i2i2-22-20000000000000000
χ574-444-4-4-44-4400-44004i−4i000−4i4i000000000000000000000000000000000000000000
χ584-444-4-4-44-4400-4400−4i4i0004i−4i000000000000000000000000000000000000000000
χ594-44-44-44-444-44-4-4-440000400-400000000000000000000000000000000000000000
χ604-44-44-44-4-4-4-4444-440000-400400000000000000000000000000000000000000000
χ614-4-4-4-4444004-400-44000000000000000000000000022−22−222200000000000000000000
χ624-4-4-4-4444004-400-440000000000000000000000000−222222−2200000000000000000000
χ634-4-4-4-444400-44004-40000000000000000000000000000022−22−22220000000000000000
χ644-4-4-4-444400-44004-400000000000000000000000000000−222222−220000000000000000
χ658-8-8888-8-8000000000000000000000000000000000000000000000000000000000

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