Finite Group Databasebeta

← Group #347589

Character table — Group #347589

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222444444444444444444448888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444222244444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-111-1-1
χ1011111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111-1-111
χ1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-111-1-111-1-1-1-111-1-111
χ1211111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222222-2-222222222-2-2-2-22222-2-2-2-20000-2-20000000000000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000220000000000000000000000000000
χ19222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000220000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-222222222-2-2220000-2-20000000000000000000000000000
χ2122222222-2-2-2-22-222-2-2000022-2-200002-200002200000022-2-2-2-2000000000000000000
χ2222222222-2-2-2-22-222-2-2000022-2-200002-20000-2-2000000-2-22222000000000000000000
χ2322222222-2-2-2-22-2-2-2220000-2-22200002-2000022000000-2-222-2-2000000000000000000
χ2422222222-2-2-2-22-2-2-2220000-2-22200002-20000-2-200000022-2-222000000000000000000
χ2522222222-2-2-2-2-2222-2-20000-2-2220000-220022000022-2-2000000-2-20000000000000000
χ2622222222-2-2-2-2-2222-2-20000-2-2220000-2200-2-20000-2-222000000220000000000000000
χ2722222222-2-2-2-2-22-2-222000022-2-20000-2200220000-2-222000000-2-20000000000000000
χ2822222222-2-2-2-2-22-2-222000022-2-20000-2200-2-2000022-2-2000000220000000000000000
χ292-222-2-2-2222-2-2002-22-22i2i−2i−2i00002i2i−2i−2i0000000000000000000000000000002−22−2i2−i2i2−i2
χ302-222-2-2-2222-2-2002-22-22i2i−2i−2i00002i2i−2i−2i000000000000000000000000000000−22−22−i2i2−i2i2
χ312-222-2-2-2222-2-2002-22-2−2i−2i2i2i0000−2i−2i2i2i0000000000000000000000000000002−22−2−i2i2−i2i2
χ322-222-2-2-2222-2-2002-22-2−2i−2i2i2i0000−2i−2i2i2i000000000000000000000000000000−22−22i2−i2i2−i2
χ332-222-2-2-2222-2-200-22-222i2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000002−2−22i2−i2−i2i2
χ342-222-2-2-2222-2-200-22-222i2i−2i−2i0000−2i−2i2i2i000000000000000000000000000000−222−2−i2i2i2−i2
χ352-222-2-2-2222-2-200-22-22−2i−2i2i2i00002i2i−2i−2i0000000000000000000000000000002−2−22−i2i2i2−i2
χ362-222-2-2-2222-2-200-22-22−2i−2i2i2i00002i2i−2i−2i000000000000000000000000000000−222−2i2−i2−i2i2
χ372-2-2-222-222-22-22-20000000000002i−2i2i−2i-22002-22i−2i2i−2i000000002i−2i2-20000000000000000
χ382-2-2-222-222-22-22-20000000000002i−2i2i−2i-2200-22−2i2i2i−2i00000000−2i2i-220000000000000000
χ392-2-2-222-222-22-22-2000000000000−2i2i−2i2i-22002-2−2i2i−2i2i00000000−2i2i2-20000000000000000
χ402-2-2-222-222-22-22-2000000000000−2i2i−2i2i-2200-222i−2i−2i2i000000002i−2i-220000000000000000
χ412-2-2-222-222-22-2-220000000000002i−2i2i−2i2-2000000−2i2i2i−2i2i−2i2-22-200000000000000000000
χ422-2-2-222-222-22-2-220000000000002i−2i2i−2i2-2000000−2i2i−2i2i−2i2i-22-2200000000000000000000
χ432-2-2-222-222-22-2-22000000000000−2i2i−2i2i2-20000002i−2i2i−2i2i−2i-22-2200000000000000000000
χ442-2-2-222-222-22-2-22000000000000−2i2i−2i2i2-20000002i−2i−2i2i−2i2i2-22-200000000000000000000
χ452-2-2-222-22-22-222200002-22-200000000-2-22-2002i−2i002i−2i−2i2i0000−2i2i000000000000000000
χ462-2-2-222-22-22-222200002-22-200000000-2-22-200−2i2i00−2i2i2i−2i00002i−2i000000000000000000
χ472-2-2-222-22-22-22220000-22-2200000000-2-2-22002i−2i00−2i2i2i−2i0000−2i2i000000000000000000
χ482-2-2-222-22-22-22220000-22-2200000000-2-2-2200−2i2i002i−2i−2i2i00002i−2i000000000000000000
χ492-2-2-222-22-22-22-2-200002-22-20000000022-222-2000000002-2-2200-220000000000000000
χ502-2-2-222-22-22-22-2-200002-22-20000000022-22-2200000000-222-2002-20000000000000000
χ512-2-2-222-22-22-22-2-20000-22-2200000000222-22-200000000-222-200-220000000000000000
χ522-2-2-222-22-22-22-2-20000-22-2200000000222-2-22000000002-2-22002-20000000000000000
χ5344-4-4-4-4444-4-44000000000000004-4-4400000000000000000000000000000000000000
χ5444-4-4-4-4444-4-4400000000000000-444-400000000000000000000000000000000000000
χ5544-4-4-4-444-444-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5644-4-4-4-444-444-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ574-444-4-4-44-4-444004-4-4400000000000000000000000000000000000000000000000000
χ584-444-4-4-44-4-44400-444-400000000000000000000000000000000000000000000000000
χ594-44-44-44-400000000000000004-4000000000000000000000000002i−2i2i−2i000000000000
χ604-44-44-44-400000000000000004-400000000000000000000000000−2i2i−2i2i000000000000
χ614-44-44-44-40000000000000000-44000000000000000000000000002i−2i−2i2i000000000000
χ624-44-44-44-40000000000000000-4400000000000000000000000000−2i2i2i−2i000000000000
χ634-4-44-444-4000000000000004-4000000000000000000000000000000002i−2i2i−2i00000000
χ644-4-44-444-4000000000000004-400000000000000000000000000000000−2i2i−2i2i00000000
χ654-4-44-444-400000000000000-44000000000000000000000000000000002i−2i−2i2i00000000
χ664-4-44-444-400000000000000-4400000000000000000000000000000000−2i2i2i−2i00000000
χ67888-8-88-8-8000000000000000000000000000000000000000000000000000000000000
χ6888-888-8-8-8000000000000000000000000000000000000000000000000000000000000

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