Finite Group Databasebeta

← Group #167313

Character table — Group #167313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444422444444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ31111111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-1-1-1
χ41111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111111111111111111111-1-1-11-1-1-1-11-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1111111
χ7111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-11-1-11111
χ8111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-11111-1-1-1-11111-1-1-1-11-1-1-111111-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1-11-111-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-11-1-111-11-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-111111111-1-1-1-111-11-1-1-1-1-111111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-111
χ1411111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ1722222222222222222-2-2-2-2-22-2222200-2000000000000000000-20-20000000000000
χ1822222222222222222-2-2-2-2-22-2-2-2-2-200-20000000000000000002020000000000000
χ19222222222222-2-2-2-2-2222-2-2-22000000-200000000000000000002002-2000-2000000
χ20222222222222-2-2-2-2-2222-2-2-22000000-20000000000000000000-200-220002000000
χ21222222222222-2-2-2-2-2-2-2-222-2-20000222-2-2000000000000000000020000-20000000
χ22222222222222-2-2-2-2-2-2-2-222-2-20000-2-22220000000000000000000-2000020000000
χ2322222222-2-2-2-22222-22-2-2-2-2-2200000020000000000000000000200-22000-2000000
χ2422222222-2-2-2-22222-22-2-2-2-2-2200000020000000000000000000-2002-20002000000
χ2522222222-2-2-2-22222-2-22222-2-2000022-2220000000000000000000-20000-20000000
χ2622222222-2-2-2-22222-2-22222-2-20000-2-2-2-2-200000000000000000002000020000000
χ2722222222-2-2-2-2-2-2-2-22-222-2-22-222-2-2002000000000000000000-2020000000000000
χ2822222222-2-2-2-2-2-2-2-22-222-2-22-2-2-22200200000000000000000020-20000000000000
χ292222-2-2-2-222-2-222-2-2200000-202-22-2000000000000022−2−222−2−20000000000002−22−2
χ302222-2-2-2-222-2-222-2-2200000-202-22-20000000000000−2−222−2−222000000000000−22−22
χ312222-2-2-2-222-2-222-2-2200000-20-22-22000000000000022−2−222−2−2000000000000−22−22
χ322222-2-2-2-222-2-222-2-2200000-20-22-220000000000000−2−222−2−2220000000000002−22−2
χ332222-2-2-2-2-2-222-2-222200000-202-2-22000000000000022−2−2−2−2220000000000002−2−22
χ342222-2-2-2-2-2-222-2-222200000-202-2-220000000000000−2−22222−2−2000000000000−222−2
χ352222-2-2-2-2-2-222-2-222200000-20-222-2000000000000022−2−2−2−222000000000000−222−2
χ362222-2-2-2-2-2-222-2-222200000-20-222-20000000000000−2−22222−2−20000000000002−2−22
χ3722-2-22-2-2200002i−2i2i−2i002i−2i2-20000002i−2i02-2i2i2−i2−i222−2−22−22−2i2−i2i2−i20000000000000000
χ3822-2-22-2-2200002i−2i2i−2i002i−2i2-20000002i−2i02-2−i2−i2i2i2−2−222−22−22−i2i2−i2i20000000000000000
χ3922-2-22-2-2200002i−2i2i−2i002i−2i2-2000000−2i2i0-22i2i2−i2−i222−2−2−22−22−i2i2−i2i20000000000000000
χ4022-2-22-2-2200002i−2i2i−2i002i−2i2-2000000−2i2i0-22−i2−i2i2i2−2−2222−22−2i2−i2i2−i20000000000000000
χ4122-2-22-2-220000−2i2i−2i2i00−2i2i2-20000002i−2i0-22i2i2−i2−i2−2−2222−22−2−i2i2−i2i20000000000000000
χ4222-2-22-2-220000−2i2i−2i2i00−2i2i2-20000002i−2i0-22−i2−i2i2i222−2−2−22−22i2−i2i2−i20000000000000000
χ4322-2-22-2-220000−2i2i−2i2i00−2i2i2-2000000−2i2i02-2i2i2−i2−i2−2−222−22−22i2−i2i2−i20000000000000000
χ4422-2-22-2-220000−2i2i−2i2i00−2i2i2-2000000−2i2i02-2−i2−i2i2i222−2−22−22−2−i2i2−i2i20000000000000000
χ454444-4-4-4-444-4-4-4-444-4000004000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-44444-4-4-4000004000000000000000000000000000000000000000000
χ4744-4-44-4-4400004i−4i4i−4i00−4i4i-440000000000000000000000000000000000000000000
χ4844-4-44-4-440000−4i4i−4i4i004i−4i-440000000000000000000000000000000000000000000
χ4944-4-4-444-400004i−4i−4i4i00000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ5044-4-4-444-400004i−4i−4i4i0000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ5144-4-4-444-40000−4i4i4i−4i00000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ5244-4-4-444-40000−4i4i4i−4i0000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ534-44-444-4-4000000000400000-400000000022−2222−220000000000000000000000000000
χ544-44-444-4-4000000000400000-4000000000−2222−22220000000000000000000000000000
χ554-44-444-4-4000000000-400000400000000000002i2−2i22i2−2i2000000000000000000000000
χ564-44-444-4-4000000000-40000040000000000000−2i22i2−2i22i2000000000000000000000000
χ574-4-444-44-44-44-40000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ584-4-444-44-44-44-4000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ594-4-444-44-4-44-440000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ604-4-444-44-4-44-44000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ614-4-44-44-444-4-4400000000000000000000000000000000000000000002-2002-20000
χ624-4-44-44-444-4-440000000000000000000000000000000000000000000-2200-220000
χ634-4-44-44-44-444-400000000000000000000000000000000000000000002-200-220000
χ644-4-44-44-44-444-40000000000000000000000000000000000000000000-22002-20000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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