Finite Group Databasebeta

← Group #167274

Character table — Group #167274

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-11111-111-1-1-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1111111
χ911111111-1-1-1-1-1-1-1-11-1-11111111-1-111-1-1-11111-1-1-1-11111-1-1-1-1-11-111-1-111-11-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-11111111-1-111-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1-11111-11-1-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-11-1-1111-11-11-1-111
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1111-1-11-11-1111-1-1
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-11111-1-1-11111-1-1-1-1-1-1-1-111111-11-1-111-11-1-1111-1-1
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-11111-1-1-1-1-1-1-111111111-1-1-1-11-1111-1-1-11-1-11-1-111
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-111-11111-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-1-111
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-111-1-1-1-1-111111111-1-1-1-111-1-1-111-1-111-111-1-1
χ172222222222222222-2-2-22-2-2-2200002222-2000000000000000000000000-2-2000000
χ182222222222222222-2-2-22-2-2-220000-2-2-2-2-200000000000000000000000022000000
χ19222222222222-2-2-2-2222-2-2-22-222220000-20000000000000000-2000000-200000000
χ20222222222222-2-2-2-2222-2-2-22-2-2-2-2-20000-200000000000000002000000200000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2000000002000000000000000002-20000000-220000
χ22222222222222-2-2-2-2-2-2-2-222-2-200000000200000000000000000-2200000002-20000
χ2322222222-2-2-2-222222-2-2-2-2-22-222-2-20000200000000000000002000000-200000000
χ2422222222-2-2-2-222222-2-2-2-2-22-2-2-222000020000000000000000-2000000200000000
χ2522222222-2-2-2-22222-222-222-2-200000000-200000000000000000220000000-2-20000
χ2622222222-2-2-2-22222-222-222-2-200000000-200000000000000000-2-20000000220000
χ2722222222-2-2-2-2-2-2-2-2-2222-2-2-22000022-2-22000000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2222-2-2-220000-2-22220000000000000000000000002-2000000
χ292222-2-2-2-222-2-2000022-2000-202-22-20000022−2−222−2−222−2−222−2−20000000000000000
χ302222-2-2-2-222-2-2000022-2000-202-22-200000−2−222−2−222−2−222−2−2220000000000000000
χ312222-2-2-2-222-2-2000022-2000-20-22-220000022−2−222−2−2−2−222−2−2220000000000000000
χ322222-2-2-2-222-2-2000022-2000-20-22-2200000−2−222−2−22222−2−222−2−20000000000000000
χ332222-2-2-2-2-2-22200002-22000-202-2-220000022−2−2−2−22222−2−2−2−2220000000000000000
χ342222-2-2-2-2-2-22200002-22000-202-2-2200000−2−22222−2−2−2−22222−2−20000000000000000
χ352222-2-2-2-2-2-22200002-22000-20-222-20000022−2−2−2−222−2−22222−2−20000000000000000
χ362222-2-2-2-2-2-22200002-22000-20-222-200000−2−22222−2−222−2−2−2−2220000000000000000
χ3722-2-22-22-22-22-222-2-2000-2000200002-22-20i2−i2i2−i2i2−i2i2−i200000000000000000000i2−i2i2−i2
χ3822-2-22-22-22-22-222-2-2000-2000200002-22-20−i2i2−i2i2−i2i2−i2i200000000000000000000−i2i2−i2i2
χ3922-2-22-22-22-22-222-2-2000-200020000-22-220i2−i2i2−i2i2−i2i2−i200000000000000000000−i2i2−i2i2
χ4022-2-22-22-22-22-222-2-2000-200020000-22-220−i2i2−i2i2−i2i2−i2i200000000000000000000i2−i2i2−i2
χ4122-2-22-22-2-22-22-2-222000-2000200002-2-220i2−i2i2−i2−i2i2−i2i200000000000000000000i2−i2−i2i2
χ4222-2-22-22-2-22-22-2-222000-2000200002-2-220−i2i2−i2i2i2−i2i2−i200000000000000000000−i2i2i2−i2
χ4322-2-22-22-2-22-22-2-222000-200020000-222-20i2−i2i2−i2−i2i2−i2i200000000000000000000−i2i2i2−i2
χ4422-2-22-22-2-22-22-2-222000-200020000-222-20−i2i2−i2i2i2−i2i2−i200000000000000000000i2−i2−i2i2
χ454444-4-4-4-444-4-40000-4-440004000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-4440000-44-40004000000000000000000000000000000000000000000
χ4744-4-44-44-44-44-4-4-4440004000-400000000000000000000000000000000000000000
χ4844-4-44-44-4-44-4444-4-40004000-400000000000000000000000000000000000000000
χ4944-4-4-44-444-4-440000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ5044-4-4-44-444-4-44000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ5144-4-4-44-44-444-40000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ5244-4-4-44-44-444-4000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ534-44-44-4-440000000000004-4000000000000000000000002i2−2i22i2−2i20000000000000000
χ544-44-44-4-440000000000004-400000000000000000000000−2i22i2−2i22i20000000000000000
χ554-44-44-4-44000000000000-4400000000000000000002i2−2i22i2−2i200000000000000000000
χ564-44-44-4-44000000000000-440000000000000000000−2i22i2−2i22i200000000000000000000
χ574-44-4-444-400004-44-400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ584-44-4-444-400004-44-40000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ594-44-4-444-40000-44-4400000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ604-44-4-444-40000-44-440000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ614-4-44-4-44400004-4-440000000000000000000000000000000000002-22-2000000000
χ624-4-44-4-44400004-4-44000000000000000000000000000000000000-22-22000000000
χ634-4-44-4-4440000-444-40000000000000000000000000000000000002-2-22000000000
χ644-4-44-4-4440000-444-4000000000000000000000000000000000000-222-2000000000
χ658-8-8888-8-8000000000000000000000000000000000000000000000000000000000

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