Finite Group Databasebeta

← Group #235723

Character table — Group #235723

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888822444444888888882222222244448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222222222-2-22222-2-2-2-2-2-22-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ18222222222222222-2-22222-2-2-2-2-2-22-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ19222222222222-2-2-222-2-2-2-2-2-2-2-222-2-222-200000000000000000000000000000000000000002-22-20000
χ20222222222222-2-2-222-2-2-2-2-2-2-2-222-2-222-20000000000000000000000000000000000000000-22-220000
χ21222222222222-2-2-2-2-2-2-2-2-22222-2-2-22-2-22000000000000000000000000000000002-22-2000000000000
χ22222222222222-2-2-2-2-2-2-2-2-22222-2-2-22-2-2200000000000000000000000000000000-22-22000000000000
χ2322222222-2-2-2-2222-2-2-2-2-2-22222-2-22-222-2000000000000000022-2-2-2-222000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-2-2-22222-2-22-222-20000000000000000-2-22222-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2222222222222-2-2-2-2-200000000000000000000000000000000000000002-2-220000
χ2622222222-2-2-2-2-2-2-2222222222222-2-2-2-2-20000000000000000000000000000000000000000-222-20000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-22222000000000000000000000000000000002-2-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2222200000000000000000000000000000000-222-2000000000000
χ292222-2-2-2-222-2-222-20022-2-2000000-200002222−2−2−2−22222−2−2−2−2002i−2i002i−2ii2i2−i2−i2i2i2−i2−i20000000000000000
χ302222-2-2-2-222-2-222-20022-2-2000000-200002222−2−2−2−22222−2−2−2−200−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i20000000000000000
χ312222-2-2-2-222-2-222-20022-2-2000000-20000−2−2−2−22222−2−2−2−22222002i−2i002i−2i−i2−i2i2i2−i2−i2i2i20000000000000000
χ322222-2-2-2-222-2-222-20022-2-2000000-20000−2−2−2−22222−2−2−2−2222200−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i20000000000000000
χ332222-2-2-2-2-2-22222-200-2-222000000-200002222−2−2−2−2−2−2−2−22222002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i20000000000000000
χ342222-2-2-2-2-2-22222-200-2-222000000-200002222−2−2−2−2−2−2−2−2222200−2i2i002i−2i−i2−i2i2i2i2i2−i2−i20000000000000000
χ352222-2-2-2-2-2-22222-200-2-222000000-20000−2−2−2−222222222−2−2−2−2002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i20000000000000000
χ362222-2-2-2-2-2-22222-200-2-222000000-20000−2−2−2−222222222−2−2−2−200−2i2i002i−2ii2i2−i2−i2−i2−i2i2i20000000000000000
χ372-2-2222-2-22-22-22-22222-22-222-2-2-2-2-222-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ382-2-2222-2-22-22-22-22222-22-222-2-2-2-2-222-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ392-2-2222-2-22-22-22-22-2-22-22-2-2-22222-2-2-22222-2-222-2-222-2-222-2-200000000000000000000000000000000
χ402-2-2222-2-22-22-22-22-2-22-22-2-2-22222-2-2-222-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ412-2-2222-2-22-22-2-22-222-22-22-2-222-2-22-22-220000000000000000000000000000000000002-22-200000000
χ422-2-2222-2-22-22-2-22-222-22-22-2-222-2-22-22-22000000000000000000000000000000000000-22-2200000000
χ432-2-2222-2-22-22-2-22-2-2-2-22-2222-2-22222-22-2000000000000000000000000000000000000000000002-22-2
χ442-2-2222-2-22-22-2-22-2-2-2-22-2222-2-22222-22-200000000000000000000000000000000000000000000-22-22
χ452-2-2222-2-2-22-222-2222-22-22-2-222-2-2-22-22-20000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ462-2-2222-2-2-22-222-2222-22-22-2-222-2-2-22-22-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ472-2-2222-2-2-22-222-22-2-2-22-2222-2-222-2-22-2222-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ482-2-2222-2-2-22-222-22-2-2-22-2222-2-222-2-22-22-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ492-2-2222-2-2-22-22-22-2222-22-222-2-2-2-22-2-2220000000000000000000000000000000000002-2-2200000000
χ502-2-2222-2-2-22-22-22-2222-22-222-2-2-2-22-2-222000000000000000000000000000000000000-222-200000000
χ512-2-2222-2-2-22-22-22-2-2-22-22-2-2-22222222-2-2000000000000000000000000000000000000000000002-2-22
χ522-2-2222-2-2-22-22-22-2-2-22-22-2-2-22222222-2-200000000000000000000000000000000000000000000-222-2
χ532-2-22-2-2222-2-222-2-2002-2-220000002000022−2−2−2−22222−2−2−2−2222-2002-2002−2−222−2−220000000000000000
χ542-2-22-2-2222-2-222-2-2002-2-220000002000022−2−2−2−22222−2−2−2−222-2200-2200−222−2−222−20000000000000000
χ552-2-22-2-2222-2-222-2-2002-2-2200000020000−2−22222−2−2−2−22222−2−22-2002-200−222−2−222−20000000000000000
χ562-2-22-2-2222-2-222-2-2002-2-2200000020000−2−22222−2−2−2−22222−2−2-2200-22002−2−222−2−220000000000000000
χ572-2-22-2-222-222-22-2-200-222-20000002000022−2−2−2−222−2−22222−2−22-200-22002−2−22−222−20000000000000000
χ582-2-22-2-222-222-22-2-200-222-20000002000022−2−2−2−222−2−22222−2−2-22002-200−222−22−2−220000000000000000
χ592-2-22-2-222-222-22-2-200-222-200000020000−2−22222−2−222−2−2−2−2222-200-2200−222−22−2−220000000000000000
χ602-2-22-2-222-222-22-2-200-222-200000020000−2−22222−2−222−2−2−2−222-22002-2002−2−22−222−20000000000000000
χ614444-4-4-4-444-4-4-4-4400-4-44400000040000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-444-4-440044-4-400000040000000000000000000000000000000000000000000000000000
χ6344-4-44-44-400000000000004-44-400000002-22-22-22-22-22-22-22-200000000000000000000000000000000
χ6444-4-44-44-400000000000004-44-40000000-22-22-22-22-22-22-22-2200000000000000000000000000000000
χ6544-4-44-44-40000000000000-44-4400000002-22-22-22-2-22-22-22-2200000000000000000000000000000000
χ6644-4-44-44-40000000000000-44-440000000-22-22-22-222-22-22-22-200000000000000000000000000000000
χ6744-4-4-44-4400000004-4000000004-4000000000000022−2222−22−2222−222200000000000000000000000000000000
χ6844-4-4-44-4400000004-4000000004-40000000000000−2222−222222−2222−2200000000000000000000000000000000
χ6944-4-4-44-440000000-4400000000-440000022−2222−22−2222−22220000000000000000000000000000000000000000
χ7044-4-4-44-440000000-4400000000-4400000−2222−222222−2222−220000000000000000000000000000000000000000
χ714-44-44-4-4400000000000004-4-4400000002-2-222-2-22-222-2-222-200000000000000000000000000000000
χ724-44-44-4-4400000000000004-4-440000000-222-2-222-22-2-222-2-2200000000000000000000000000000000
χ734-44-44-4-440000000000000-444-400000002-2-222-2-222-2-222-2-2200000000000000000000000000000000
χ744-44-44-4-440000000000000-444-40000000-222-2-222-2-222-2-222-200000000000000000000000000000000
χ754-44-4-444-400000004-400000000-440000022−22−2222−222222−220000000000000000000000000000000000000000
χ764-44-4-444-400000004-400000000-4400000−222222−2222−22−22220000000000000000000000000000000000000000
χ774-44-4-444-40000000-44000000004-4000000000000022−22−2222−222222−2200000000000000000000000000000000
χ784-44-4-444-40000000-44000000004-40000000000000−222222−2222−22−222200000000000000000000000000000000
χ794-4-44-4-4444-4-44-44400-444-4000000-40000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-444-4-444004-4-44000000-40000000000000000000000000000000000000000000000000000

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