Finite Group Databasebeta

← Group #167368

Character table — Group #167368

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ5111111111111111111111111-1-1-1-1111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ7111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-111-111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-11-1-11111111-1-111-1-1-11111-1-1-1-11111-1-1-1-11-111-1-11-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-11111111-1-111-1-1-1-1-1-1-11111-1-1-1-111111-111-1-11-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-111-11-1-11111-1-1
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-111-1111-1-1-1-111
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-11111-1-1-11111-1-1-1-11111-1-1-1-1-111-11-1-11-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-11111-1-1-1-1-1-1-11111-1-1-1-11111-111-11-1-1111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-1111111-1-1-1-1-1-1-1-11111-11-11-111-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-11-11-111-1-1-11111-1-1
χ1722222222222222222-2-2-2-2-2-22222200-2000000000000000000-2-200000000000000
χ1822222222222222222-2-2-2-2-2-22-2-2-2-200-20000000000000000002200000000000000
χ19222222222222-2-2-2-2-22222-2-2-2000022-222000000000000000000-200-20000000000
χ20222222222222-2-2-2-2-22222-2-2-20000-2-2-2-2-200000000000000000020020000000000
χ21222222222222-2-2-2-2-2-2-2-2-222-200000020000000000000000000002-20-2200000000
χ22222222222222-2-2-2-2-2-2-2-2-222-20000002000000000000000000000-2202-200000000
χ2322222222-2-2-2-22222-222-2-222-2000000-2000000000000000000000220-2-200000000
χ2422222222-2-2-2-22222-222-2-222-2000000-2000000000000000000000-2-202200000000
χ2522222222-2-2-2-22222-2-2-222-2-2-20000222-2-2000000000000000000-20020000000000
χ2622222222-2-2-2-22222-2-2-222-2-2-20000-2-2222000000000000000000200-20000000000
χ2722222222-2-2-2-2-2-2-2-2222-2-2-2-2222-2-2002000000000000000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2-2222-2-2-2-22-2-2220020000000000000000002-200000000000000
χ292222-2-2-2-222-2-222-2-22000000-22-22-20000022−2−222−2−2000000000000000000002−22−2
χ302222-2-2-2-222-2-222-2-22000000-22-22-200000−2−222−2−22200000000000000000000−22−22
χ312222-2-2-2-222-2-222-2-22000000-2-22-220000022−2−222−2−200000000000000000000−22−22
χ322222-2-2-2-222-2-222-2-22000000-2-22-2200000−2−222−2−222000000000000000000002−22−2
χ332222-2-2-2-2-2-222-2-2222000000-22-2-220000022−2−2−2−222000000000000000000002−2−22
χ342222-2-2-2-2-2-222-2-2222000000-22-2-2200000−2−22222−2−200000000000000000000−222−2
χ352222-2-2-2-2-2-222-2-2222000000-2-222-20000022−2−2−2−22200000000000000000000−222−2
χ362222-2-2-2-2-2-222-2-2222000000-2-222-200000−2−22222−2−2000000000000000000002−2−22
χ372-22-22-22-22i−2i2i−2i000002i−2i2-200000002i−2i02-2i2−i2i2−i22−22−222−2−2i2i2−i2−i20000000000000000
χ382-22-22-22-22i−2i2i−2i000002i−2i2-200000002i−2i02-2−i2i2−i2i2−22−22−2−222−i2−i2i2i20000000000000000
χ392-22-22-22-22i−2i2i−2i000002i−2i2-20000000−2i2i0-22i2−i2i2−i22−22−2−2−222−i2−i2i2i20000000000000000
χ402-22-22-22-22i−2i2i−2i000002i−2i2-20000000−2i2i0-22−i2i2−i2i2−22−2222−2−2i2i2−i2−i20000000000000000
χ412-22-22-22-2−2i2i−2i2i00000−2i2i2-200000002i−2i0-22i2−i2i2−i2−22−2222−2−2−i2−i2i2i20000000000000000
χ422-22-22-22-2−2i2i−2i2i00000−2i2i2-200000002i−2i0-22−i2i2−i2i22−22−2−2−222i2i2−i2−i20000000000000000
χ432-22-22-22-2−2i2i−2i2i00000−2i2i2-20000000−2i2i02-2i2−i2i2−i2−22−22−2−222i2i2−i2−i20000000000000000
χ442-22-22-22-2−2i2i−2i2i00000−2i2i2-20000000−2i2i02-2−i2i2−i2i22−22−222−2−2−i2−i2i2i20000000000000000
χ454444-4-4-4-444-4-4-4-444-4000000400000000000000000000000000000000000000000
χ464444-4-4-4-4-4-44444-4-4-4000000400000000000000000000000000000000000000000
χ4744-4-4-4-44400000000000004-40000000000000000002i2−2i22i2−2i200000000000000000000
χ4844-4-4-4-44400000000000004-4000000000000000000−2i22i2−2i22i200000000000000000000
χ4944-4-4-4-4440000000000000-4400000000000000000000002i2−2i22i2−2i20000000000000000
χ5044-4-4-4-4440000000000000-440000000000000000000000−2i22i2−2i22i20000000000000000
χ514-44-44-44-44i−4i4i−4i00000−4i4i-4400000000000000000000000000000000000000000000
χ524-44-44-44-4−4i4i−4i4i000004i−4i-4400000000000000000000000000000000000000000000
χ534-44-4-44-444i−4i−4i4i0000000000000000000002i−2i−2i2i2-2-22000000000000000000000000
χ544-44-4-44-444i−4i−4i4i000000000000000000000−2i2i2i−2i-222-2000000000000000000000000
χ554-44-4-44-44−4i4i4i−4i0000000000000000000002i−2i−2i2i-222-2000000000000000000000000
χ564-44-4-44-44−4i4i4i−4i000000000000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ574-4-444-4-4400004i−4i4i−4i000000000000000000000000000000000000000002i−2i2-20000
χ584-4-444-4-4400004i−4i4i−4i00000000000000000000000000000000000000000−2i2i-220000
χ594-4-444-4-440000−4i4i−4i4i000000000000000000000000000000000000000002i−2i-220000
χ604-4-444-4-440000−4i4i−4i4i00000000000000000000000000000000000000000−2i2i2-20000
χ614-4-44-444-400004i−4i−4i4i00000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ624-4-44-444-400004i−4i−4i4i0000000000000000000000000−2i2i2i−2i-222-20000000000000000
χ634-4-44-444-40000−4i4i4i−4i00000000000000000000000002i−2i−2i2i-222-20000000000000000
χ644-4-44-444-40000−4i4i4i−4i0000000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ6588-8-888-8-8000000000000000000000000000000000000000000000000000000000

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