Finite Group Databasebeta

← Group #167683

Character table — Group #167683

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422444444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1
χ311111111111111111111111111-1-11-1-1111111111111111111-11-1-11-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1111111
χ5111111111111111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1
χ6111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-11-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1111-111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-111-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-11-11-1-1111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-11-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-111-1-1-1-111111111-1-1-1-111-1-1-111-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-1-1-1-1-111111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1111-1-1-1-111
χ172222222222222222-2-2-222-2-2-20022-22200000000000000000000000-2000-2000000
χ182222222222222222-2-2-222-2-2-200-2-2-2-2-20000000000000000000000020002000000
χ19222222222222-2-2-2-222-2-2-222-22200-2002200000000000000000-200-200000000000
χ20222222222222-2-2-2-222-2-2-222-2-2-200-200-2-200000000000000000200200000000000
χ21222222222222-2-2-2-2-2-22-2-2-2-220000200000000000000000000202-200-2000000000
χ22222222222222-2-2-2-2-2-22-2-2-2-220000200000000000000000000-20-22002000000000
χ2322222222-2-2-2-22222222-2-2-2-220000-20000000000000000000020-2200-2000000000
χ2422222222-2-2-2-22222222-2-2-2-220000-200000000000000000000-202-2002000000000
χ2522222222-2-2-2-22222-2-2-2-2-222-22200200-2-200000000000000000200-200000000000
χ2622222222-2-2-2-22222-2-2-2-2-222-2-2-2002002200000000000000000-200200000000000
χ2722222222-2-2-2-2-2-2-2-222-222-2-2-200222-2-200000000000000000000000-20002000000
χ2822222222-2-2-2-2-2-2-2-222-222-2-2-200-2-2222000000000000000000000002000-2000000
χ292-22-2-222-22i2i−2i−2i2i2i−2i−2i0002-2000002i−2i02-20000000000i2i2−i2−i222−2−20000000000002−2i2−i2
χ302-22-2-222-22i2i−2i−2i2i2i−2i−2i0002-2000002i−2i02-20000000000−i2−i2i2i2−2−222000000000000−22−i2i2
χ312-22-2-222-22i2i−2i−2i2i2i−2i−2i0002-200000−2i2i0-220000000000i2i2−i2−i222−2−2000000000000−22−i2i2
χ322-22-2-222-22i2i−2i−2i2i2i−2i−2i0002-200000−2i2i0-220000000000−i2−i2i2i2−2−2220000000000002−2i2−i2
χ332-22-2-222-2−2i−2i2i2i−2i−2i2i2i0002-2000002i−2i0-220000000000i2i2−i2−i2−2−2220000000000002−2−i2i2
χ342-22-2-222-2−2i−2i2i2i−2i−2i2i2i0002-2000002i−2i0-220000000000−i2−i2i2i222−2−2000000000000−22i2−i2
χ352-22-2-222-2−2i−2i2i2i−2i−2i2i2i0002-200000−2i2i02-20000000000i2i2−i2−i2−2−222000000000000−22i2−i2
χ362-22-2-222-2−2i−2i2i2i−2i−2i2i2i0002-200000−2i2i02-20000000000−i2−i2i2i222−2−20000000000002−2−i2i2
χ372-2-2222-2-22i−2i2i−2i00002i−2i0002-202-2000002i−2i22−2−2i2i2−i2−i22−22−2i2−i2i2−i20000000000000000
χ382-2-2222-2-22i−2i2i−2i00002i−2i0002-202-2000002i−2i−2−222−i2−i2i2i2−22−22−i2i2−i2i20000000000000000
χ392-2-2222-2-22i−2i2i−2i00002i−2i0002-20-2200000−2i2i22−2−2i2i2−i2−i2−22−22−i2i2−i2i20000000000000000
χ402-2-2222-2-22i−2i2i−2i00002i−2i0002-20-2200000−2i2i−2−222−i2−i2i2i22−22−2i2−i2i2−i20000000000000000
χ412-2-2222-2-2−2i2i−2i2i0000−2i2i0002-202-200000−2i2i22−2−2−i2−i2i2i22−22−2−i2i2−i2i20000000000000000
χ422-2-2222-2-2−2i2i−2i2i0000−2i2i0002-202-200000−2i2i−2−222i2i2−i2−i2−22−22i2−i2i2−i20000000000000000
χ432-2-2222-2-2−2i2i−2i2i0000−2i2i0002-20-22000002i−2i22−2−2−i2−i2i2i2−22−22i2−i2i2−i20000000000000000
χ442-2-2222-2-2−2i2i−2i2i0000−2i2i0002-20-22000002i−2i−2−222i2i2−i2−i22−22−2−i2i2−i2i20000000000000000
χ454444-4-4-4-400004-44-4000000000000000002-22-22-22-2000000000000000000000000
χ464444-4-4-4-400004-44-400000000000000000-22-22-22-22000000000000000000000000
χ474444-4-4-4-40000-44-44000000000000000002-22-2-22-22000000000000000000000000
χ484444-4-4-4-40000-44-4400000000000000000-22-222-22-2000000000000000000000000
χ4944-4-4-44-444-4-44000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ5044-4-4-44-444-4-4400000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ5144-4-4-44-44-444-4000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ5244-4-4-44-44-444-400000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ534-44-44-4-4400004i−4i−4i4i00000000000000000000000000000000000000002i−2i02-20000
χ544-44-44-4-4400004i−4i−4i4i0000000000000000000000000000000000000000−2i2i0-220000
χ554-44-44-4-440000−4i4i4i−4i00000000000000000000000000000000000000002i−2i0-220000
χ564-44-44-4-440000−4i4i4i−4i0000000000000000000000000000000000000000−2i2i02-20000
χ574-44-4-444-44i4i−4i−4i−4i−4i4i4i000-4400000000000000000000000000000000000000000000
χ584-44-4-444-4−4i−4i4i4i4i4i−4i−4i000-4400000000000000000000000000000000000000000000
χ594-4-4444-4-44i−4i4i−4i0000−4i4i000-44000000000000000000000000000000000000000000
χ604-4-4444-4-4−4i4i−4i4i00004i−4i000-44000000000000000000000000000000000000000000
χ614-4-44-4-444000000000040000-400000000000002i2−2i2−2i22i2000000000000000000000000
χ624-4-44-4-444000000000040000-40000000000000−2i22i22i2−2i2000000000000000000000000
χ634-4-44-4-4440000000000-40000400000000022−22−22220000000000000000000000000000
χ644-4-44-4-4440000000000-400004000000000−222222−220000000000000000000000000000
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000

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