Finite Group Databasebeta

← Group #167659

Character table — Group #167659

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422444444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1111-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111-11-1-1-1-1-1-1-11-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111-1-11111
χ5111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1111-111-11-1-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-1-11-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-11-1-1-1-111111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1111-1111-1-11-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-11111-11-1-1-11-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1111-11-1-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-11-111-1-11-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1111-1-1-1-1-1111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1111-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-11111111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11-1-111111-1-111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111111-1-11-1-1-1-111
χ172222222222222222-2-2-2-2-222-200-2002222000000000000000000000-20000-200000
χ182222222222222222-2-2-2-2-222-200-200-2-2-2-200000000000000000000020000200000
χ19222222222222-2-2-2-2222-2-2-2-2222-222000000000000000000000-20000000-2000000
χ20222222222222-2-2-2-2222-2-2-2-22-2-2-2-2-2000000000000000000000200000002000000
χ21222222222222-2-2-2-2-2-2-222-2-2-2002000000000000000000000020-200020000-20000
χ22222222222222-2-2-2-2-2-2-222-2-2-20020000000000000000000000-202000-2000020000
χ2322222222-2-2-2-2222222-222-2-2-200-20000000000000000000000202000-20000-20000
χ2422222222-2-2-2-2222222-222-2-2-200-20000000000000000000000-20-20002000020000
χ2522222222-2-2-2-22222-2-22-2-2-2-22222-2-2000000000000000000000-200000002000000
χ2622222222-2-2-2-22222-2-22-2-2-2-22-2-222200000000000000000000020000000-2000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-222-20020022-2-200000000000000000000020000-200000
χ2822222222-2-2-2-2-2-2-2-222-2-2-222-200200-2-222000000000000000000000-20000200000
χ2922-22-22-2-222-2-200002-2-2000022-202-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3022-22-22-2-222-2-200002-2-2000022-202-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3122-22-22-2-222-2-200002-2-200002-220-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3222-22-22-2-222-2-200002-2-200002-220-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3322-22-22-2-2-2-2220000-22-2000022-20-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ3422-22-22-2-2-2-2220000-22-2000022-20-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ3522-22-22-2-2-2-2220000-22-200002-2202-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ3622-22-22-2-2-2-2220000-22-200002-2202-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ372-2-222-22-22i−2i2i−2i2i2i−2i−2i000002-20000002-22i−2i000000002−22−2i2−i2i2−i20000000000002−2i2−i2
χ382-2-222-22-22i−2i2i−2i2i2i−2i−2i000002-20000002-22i−2i00000000−22−22−i2i2−i2i2000000000000−22−i2i2
χ392-2-222-22-22i−2i2i−2i2i2i−2i−2i000002-2000000-22−2i2i000000002−22−2i2−i2i2−i2000000000000−22−i2i2
χ402-2-222-22-22i−2i2i−2i2i2i−2i−2i000002-2000000-22−2i2i00000000−22−22−i2i2−i2i20000000000002−2i2−i2
χ412-2-222-22-2−2i2i−2i2i−2i−2i2i2i000002-20000002-2−2i2i000000002−22−2−i2i2−i2i20000000000002−2−i2i2
χ422-2-222-22-2−2i2i−2i2i−2i−2i2i2i000002-20000002-2−2i2i00000000−22−22i2−i2i2−i2000000000000−22i2−i2
χ432-2-222-22-2−2i2i−2i2i−2i−2i2i2i000002-2000000-222i−2i000000002−22−2−i2i2−i2i2000000000000−22i2−i2
χ442-2-222-22-2−2i2i−2i2i−2i−2i2i2i000002-2000000-222i−2i00000000−22−22i2−i2i2−i20000000000002−2−i2i2
χ45444-44-4-4-4000000000004-4000000000000000022−2222−22000000000000000000000000
χ46444-44-4-4-4000000000004-40000000000000000−2222−2222000000000000000000000000
χ47444-44-4-4-400000000000-4400000000000022−2222−220000000000000000000000000000
χ48444-44-4-4-400000000000-44000000000000−2222−22220000000000000000000000000000
χ4944-44-44-4-444-4-40000-4440000-400000000000000000000000000000000000000000
χ5044-44-44-4-4-4-44400004-440000-400000000000000000000000000000000000000000
χ5144-4-4-4-44400004-44-4000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ5244-4-4-4-44400004-44-400000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ5344-4-4-4-4440000-44-44000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ5444-4-4-4-4440000-44-4400000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ554-444-4-4-444i−4i−4i4i000000000000000000000000000002i−2i−2i2i-222-20000000000000000
χ564-444-4-4-444i−4i−4i4i00000000000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ574-444-4-4-44−4i4i4i−4i000000000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ584-444-4-4-44−4i4i4i−4i00000000000000000000000000000−2i2i2i−2i-222-20000000000000000
χ594-44-4-444-400004i−4i−4i4i0000000000000000000000000000000000002i−2i002-20000000
χ604-44-4-444-400004i−4i−4i4i000000000000000000000000000000000000−2i2i00-220000000
χ614-44-4-444-40000−4i4i4i−4i0000000000000000000000000000000000002i−2i00-220000000
χ624-44-4-444-40000−4i4i4i−4i000000000000000000000000000000000000−2i2i002-20000000
χ634-4-444-44-44i−4i4i−4i−4i−4i4i4i00000-44000000000000000000000000000000000000000000
χ644-4-444-44-4−4i4i−4i4i4i4i−4i−4i00000-44000000000000000000000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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