Finite Group Databasebeta

← Group #296270

Character table — Group #296270

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444422444488888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-11-11-111-1-111-1-1
χ10111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111-1-111
χ11111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111-11-11-11-1-1-111-1-111
χ12111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-11-11-11-1111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111-11-1-11-1111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-11-111-11-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11-11-1-11-11-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-11-111-11-111-1-1-1-111
χ172222222222222222222222-2-2-2-2-2-2-2-2-2-222-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-222222222-2-2-2-222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222200000000000000000000000000000000
χ2122222222-2-2-2-22222-2-2000022-2-222-2-2000000000000000000000022-2-2000000000000
χ2222222222-2-2-2-22222-2-2000022-2-222-2-20000000000000000000000-2-222000000000000
χ2322222222-2-2-2-22222-2-20000-2-222-2-2220000000000000000000000000022-2-200000000
χ2422222222-2-2-2-22222-2-20000-2-222-2-22200000000000000000000000000-2-22200000000
χ2522222222-2-2-2-2-2-2-2-222000022-2-2-2-222000000000000000000000000002-2-2200000000
χ2622222222-2-2-2-2-2-2-2-222000022-2-2-2-22200000000000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2220000-2-22222-2-200000000000000000000002-2-22000000000000
χ2822222222-2-2-2-2-2-2-2-2220000-2-22222-2-20000000000000000000000-222-2000000000000
χ2922-2-222-2-22-2-2222-2-22-22i2i−2i−2i00000000002i−2i00i2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ3022-2-222-2-22-2-2222-2-22-22i2i−2i−2i00000000002i−2i00−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ3122-2-222-2-22-2-2222-2-22-2−2i−2i2i2i0000000000−2i2i00i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ3222-2-222-2-22-2-2222-2-22-2−2i−2i2i2i0000000000−2i2i00−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ3322-2-222-2-22-2-22-2-222-222i2i−2i−2i0000000000−2i2i00i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ3422-2-222-2-22-2-22-2-222-222i2i−2i−2i0000000000−2i2i00−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ3522-2-222-2-22-2-22-2-222-22−2i−2i2i2i00000000002i−2i00i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ3622-2-222-2-22-2-22-2-222-22−2i−2i2i2i00000000002i−2i00−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ372-2222-2-2-2-22-220000002i−2i2i−2i00002-22-200002i−2i00002i−2i2i−2i00002-22-20000000000000000
χ382-2222-2-2-2-22-220000002i−2i2i−2i00002-22-200002i−2i0000−2i2i−2i2i0000-22-220000000000000000
χ392-2222-2-2-2-22-220000002i−2i2i−2i0000-22-220000−2i2i2i−2i2i−2i00002-22-200000000000000000000
χ402-2222-2-2-2-22-220000002i−2i2i−2i0000-22-220000−2i2i−2i2i−2i2i0000-22-2200000000000000000000
χ412-2222-2-2-2-22-22000000−2i2i−2i2i00002-22-20000−2i2i00002i−2i2i−2i0000-22-220000000000000000
χ422-2222-2-2-2-22-22000000−2i2i−2i2i00002-22-20000−2i2i0000−2i2i−2i2i00002-22-20000000000000000
χ432-2222-2-2-2-22-22000000−2i2i−2i2i0000-22-2200002i−2i2i−2i2i−2i0000-22-2200000000000000000000
χ442-2222-2-2-2-22-22000000−2i2i−2i2i0000-22-2200002i−2i−2i2i−2i2i00002-22-200000000000000000000
χ452-2-2-22-222-2-2220000002-2-222-22-200002-200002−2−222−2−222−2−222−2−220000000000000000
χ462-2-2-22-222-2-2220000002-2-222-22-200002-20000−222−2−222−2−222−2−222−20000000000000000
χ472-2-2-22-222-2-2220000002-2-22-22-220000-2200002−2−22−222−22−2−22−222−20000000000000000
χ482-2-2-22-222-2-2220000002-2-22-22-220000-220000−222−22−2−22−222−22−2−220000000000000000
χ492-2-2-22-222-2-222000000-222-22-22-20000-2200002−2−222−2−22−222−2−222−20000000000000000
χ502-2-2-22-222-2-222000000-222-22-22-20000-220000−222−2−222−22−2−222−2−220000000000000000
χ512-2-2-22-222-2-222000000-222-2-22-2200002-200002−2−22−222−2−222−22−2−220000000000000000
χ522-2-2-22-222-2-222000000-222-2-22-2200002-20000−222−22−2−222−2−22−222−20000000000000000
χ5344-4-444-4-4-444-444-4-4-4400000000000000000000000000000000000000000000000000
χ5444-4-444-4-4-444-4-4-4444-400000000000000000000000000000000000000000000000000
χ554-4444-4-4-44-44-4000000000000004-4-4400000000000000000000000000000000000000
χ564-4444-4-4-44-44-400000000000000-444-400000000000000000000000000000000000000
χ574-44-4-444-400004-44-40000000000000000000000000000000000000000000000002i−2i2i−2i
χ584-44-4-444-400004-44-4000000000000000000000000000000000000000000000000−2i2i−2i2i
χ594-44-4-444-40000-44-440000000000000000000000000000000000000000000000002i−2i−2i2i
χ604-44-4-444-40000-44-44000000000000000000000000000000000000000000000000−2i2i2i−2i
χ614-4-44-44-4400004-4-44000000000000000000000000000000000000000000002-22-20000
χ624-4-44-44-4400004-4-4400000000000000000000000000000000000000000000-22-220000
χ634-4-44-44-440000-444-4000000000000000000000000000000000000000000002-2-220000
χ644-4-44-44-440000-444-400000000000000000000000000000000000000000000-222-20000
χ654-4-4-44-44444-4-400000000004-4-44000000000000000000000000000000000000000000
χ664-4-4-44-44444-4-40000000000-444-4000000000000000000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ6888-88-8-88-8000000000000000000000000000000000000000000000000000000000000

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