Finite Group Databasebeta

← Group #166997

Character table — Group #166997

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444422444444488888888888888882222444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-11-1-11111
χ5111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-111-1-1-1-1
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1111111
χ911111111-1-1-1-1-1-1-1-11-1-11111111-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-11-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-11111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111-111-1-11-1-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-111-11-1-11-1-111
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-111-11-1-1111-1-1
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-111-1111-1-1
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-11-1-1-111-11-1-111
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11-11-111-1-1-111
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111-11-11-111-111-1-1
χ172222222222222222-2-2-22-2-2-2200-200222200000000000000000000-2-20000000000
χ182222222222222222-2-2-22-2-2-2200-200-2-2-2-200000000000000000000220000000000
χ19222222222222-2-2-2-2222-2-2-22-222-22200000000000000000000000000-200-2000000
χ20222222222222-2-2-2-2222-2-2-22-2-2-2-2-2-2000000000000000000000000002002000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2002000000000000000000000000000002-20-220000
χ22222222222222-2-2-2-2-2-2-2-222-2-200200000000000000000000000000000-2202-20000
χ2322222222-2-2-2-222222-2-2-2-2-22-2222-2-200000000000000000000000000-2002000000
χ2422222222-2-2-2-222222-2-2-2-2-22-2-2-222200000000000000000000000000200-2000000
χ2522222222-2-2-2-22222-222-222-2-200-200000000000000000000000000000220-2-20000
χ2622222222-2-2-2-22222-222-222-2-200-200000000000000000000000000000-2-20220000
χ2722222222-2-2-2-2-2-2-2-2-2222-2-2-220020022-2-200000000000000000000-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2222-2-2-2200200-2-222000000000000000000002-20000000000
χ292222-2-2-2-222-2-20000-22-2000202-202-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ302222-2-2-2-222-2-20000-22-2000202-202-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ312222-2-2-2-222-2-20000-22-200020-220-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ322222-2-2-2-222-2-20000-22-200020-220-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ332222-2-2-2-2-2-2220000-2-22000202-20-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ342222-2-2-2-2-2-2220000-2-22000202-20-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ352222-2-2-2-2-2-2220000-2-2200020-2202-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ362222-2-2-2-2-2-2220000-2-2200020-2202-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ372-22-2-2-2222-22-222-2-2000-20002000002-22-22−22−22−22−2000000000000000000002−22−2
χ382-22-2-2-2222-22-222-2-2000-20002000002-22-2−22−22−22−2200000000000000000000−22−22
χ392-22-2-2-2222-22-222-2-2000-2000200000-22-222−22−22−22−200000000000000000000−22−22
χ402-22-2-2-2222-22-222-2-2000-2000200000-22-22−22−22−22−22000000000000000000002−22−2
χ412-22-2-2-222-22-22-2-222000-20002000002-2-222−22−2−22−22000000000000000000002−2−22
χ422-22-2-2-222-22-22-2-222000-20002000002-2-22−22−222−22−200000000000000000000−222−2
χ432-22-2-2-222-22-22-2-222000-2000200000-222-22−22−2−22−2200000000000000000000−222−2
χ442-22-2-2-222-22-22-2-222000-2000200000-222-2−22−222−22−2000000000000000000002−2−22
χ454444-4-4-4-444-4-400004-44000-4000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-444000044-4000-4000000000000000000000000000000000000000000
χ4744-4-44-44-40000000000004-4000000000000000000000002i2−2i22i2−2i20000000000000000
χ4844-4-44-44-40000000000004-400000000000000000000000−2i22i2−2i22i20000000000000000
χ4944-4-44-44-4000000000000-4400000000000000000002i2−2i22i2−2i200000000000000000000
χ5044-4-44-44-4000000000000-440000000000000000000−2i22i2−2i22i200000000000000000000
χ5144-4-4-44-4400004-44-400000000000000000000000002-2-222-2-220000000000000000
χ5244-4-4-44-4400004-44-40000000000000000000000000-222-2-222-20000000000000000
χ5344-4-4-44-440000-44-4400000000000000000000000002-2-22-222-20000000000000000
χ5444-4-4-44-440000-44-440000000000000000000000000-222-22-2-220000000000000000
χ554-44-444-4-44-4-440000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ564-44-444-4-44-4-44000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ574-44-444-4-4-444-40000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ584-44-444-4-4-444-4000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ594-44-4-4-4444-44-4-4-4440004000-400000000000000000000000000000000000000000
χ604-44-4-4-444-44-4444-4-40004000-400000000000000000000000000000000000000000
χ614-4-444-4-4400004-4-440000000000000000000000000000000002-22-2000000000000
χ624-4-444-4-4400004-4-44000000000000000000000000000000000-22-22000000000000
χ634-4-444-4-440000-444-40000000000000000000000000000000002-2-22000000000000
χ644-4-444-4-440000-444-4000000000000000000000000000000000-222-2000000000000
χ658-8-88-888-8000000000000000000000000000000000000000000000000000000000

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