Finite Group Databasebeta

← Group #304509

Character table — Group #304509

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444444444444422224444448888888888888888444444444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1
χ91111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-11-1
χ101111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-111-11
χ111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-111-11
χ121111111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-11111-1-1-11
χ141111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1111-1-1-1-1111-1
χ151111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-1-1-11-1-1-111-1-1111-1
χ161111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1111-1-111-1-1-11
χ1722222222222-2-22222-2-2-2-2-2-22222222-2-2-2-20000000000000000-2-222-2-2000000000000000000000000
χ1822222222222-2-22222-2-2-2-2-2-22-2-2-2-222-2-2-2-2000000000000000022-2-222000000000000000000000000
χ1922222222222-2-2-2-2-2-22222-2-222222-2-222-2-20000000000000000-2-2-2-222000000000000000000000000
χ2022222222222-2-2-2-2-2-22222-2-22-2-2-2-2-2-222-2-200000000000000002222-2-2000000000000000000000000
χ2122222222-2-2-2222222222222-20000-2-2-2-2-2-20000000000000000000000222200000000-2-20000000000
χ2222222222-2-2-2222222222222-20000-2-2-2-2-2-20000000000000000000000-2-2-2-200000000220000000000
χ2322222222-2-2-222-2-2-2-2-2-2-2-222-200002222-2-2000000000000000000000022-2-200000000-220000000000
χ2422222222-2-2-222-2-2-2-2-2-2-2-222-200002222-2-20000000000000000000000-2-222000000002-20000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-20000-2-222220000000000000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-20000-2-22222000000000000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-2000022-2-2220000000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-2000022-2-222000000000000000000000000000000000000-222-2000000
χ292222-2-2-2-222-20022-2-2000000-222-2-22-200002222−2−2−2−22222−2−2−2−2002-200000022−2−222−2−2000000000000
χ302222-2-2-2-222-20022-2-2000000-222-2-22-20000−2−2−2−22222−2−2−2−22222002-2000000−2−222−2−222000000000000
χ312222-2-2-2-222-20022-2-2000000-2-2-2222-200002222−2−2−2−22222−2−2−2−200-22000000−2−222−2−222000000000000
χ322222-2-2-2-222-20022-2-2000000-2-2-2222-20000−2−2−2−22222−2−2−2−2222200-2200000022−2−222−2−2000000000000
χ332222-2-2-2-222-200-2-222000000-222-2-2-2200002222−2−2−2−2−2−2−2−2222200-2200000022−2−2−2−222000000000000
χ342222-2-2-2-222-200-2-222000000-222-2-2-220000−2−2−2−222222222−2−2−2−200-22000000−2−22222−2−2000000000000
χ352222-2-2-2-222-200-2-222000000-2-2-222-2200002222−2−2−2−2−2−2−2−22222002-2000000−2−22222−2−2000000000000
χ362222-2-2-2-222-200-2-222000000-2-2-222-220000−2−2−2−222222222−2−2−2−2002-200000022−2−2−2−222000000000000
χ3722-2-22-22-22-2-22-2000000002-222-22-200002-2000000002i2i−2i−2i2i2i−2i−2i2-20000000000002i−2i2i−2i000000000000
χ3822-2-22-22-22-2-22-2000000002-222-22-200002-200000000−2i−2i2i2i−2i−2i2i2i2-2000000000000−2i2i−2i2i000000000000
χ3922-2-22-22-22-2-22-2000000002-22-22-2200002-2000000002i2i−2i−2i2i2i−2i−2i-22000000000000−2i2i−2i2i000000000000
χ4022-2-22-22-22-2-22-2000000002-22-22-2200002-200000000−2i−2i2i2i−2i−2i2i2i-220000000000002i−2i2i−2i000000000000
χ4122-2-22-22-22-2-2-2200000000-2222-22-20000-222i2i−2i−2i2i2i−2i−2i00000000-22000000002i−2i2i−2i0000000000000000
χ4222-2-22-22-22-2-2-2200000000-2222-22-20000-22−2i−2i2i2i−2i−2i2i2i00000000-2200000000−2i2i−2i2i0000000000000000
χ4322-2-22-22-22-2-2-2200000000-222-22-220000-222i2i−2i−2i2i2i−2i−2i000000002-200000000−2i2i−2i2i0000000000000000
χ4422-2-22-22-22-2-2-2200000000-222-22-220000-22−2i−2i2i2i−2i−2i2i2i000000002-2000000002i−2i2i−2i0000000000000000
χ4522-2-2-22-222-2200000022-2-200-22-2-22002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200002-20000i2−i2−i2i2i2−i2−i2i2000000000000
χ4622-2-2-22-222-2200000022-2-200-22-2-22002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200002-20000−i2i2i2−i2−i2i2i2−i2000000000000
χ4722-2-2-22-222-2200000022-2-200-2-222-2002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000-220000−i2i2i2−i2−i2i2i2−i2000000000000
χ4822-2-2-22-222-2200000022-2-200-2-222-2002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000-220000i2−i2−i2i2i2−i2−i2i2000000000000
χ4922-2-2-22-222-22000000-2-22200-22-2-2200-2200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000-220000i2−i2−i2i2−i2i2i2−i2000000000000
χ5022-2-2-22-222-22000000-2-22200-22-2-2200-2200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000-220000−i2i2i2−i2i2−i2−i2i2000000000000
χ5122-2-2-22-222-22000000-2-22200-2-222-200-2200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200002-20000−i2i2i2−i2i2−i2−i2i2000000000000
χ5222-2-2-22-222-22000000-2-22200-2-222-200-2200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200002-20000i2−i2−i2i2−i2i2i2−i2000000000000
χ532-2-222-2-22000222-22-22-22-2-2-200000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000002-22-200000000000000i2−i2i2−i200
χ542-2-222-2-22000222-22-22-22-2-2-200000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000-22-2200000000000000−i2i2−i2i200
χ552-2-222-2-22000222-22-22-22-2-2-200000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000002-22-200000000000000−i2i2−i2i200
χ562-2-222-2-22000222-22-22-22-2-2-200000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000-22-2200000000000000i2−i2i2−i200
χ572-2-222-2-2200022-22-22-22-22-2-200000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000002-2-2200000000000000i2−i2−i2i200
χ582-2-222-2-2200022-22-22-22-22-2-200000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000-222-200000000000000−i2i2i2−i200
χ592-2-222-2-2200022-22-22-22-22-2-200000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000002-2-2200000000000000−i2i2i2−i200
χ602-2-222-2-2200022-22-22-22-22-2-200000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000-222-200000000000000i2−i2−i2i200
χ614444-4-4-4-4-4-440044-4-400000040000-4400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-4400-4-444000000400004-400000000000000000000000000000000000000000000000000
χ6344-4-44-44-4-4444-4000000004-4-400000000-440000000000000000000000000000000000000000000000
χ6444-4-44-44-4-444-4400000000-44-4000000004-40000000000000000000000000000000000000000000000
χ6544-4-4-44-44-44-400000044-4-4004000000-44000000000000000000000000000000000000000000000000
χ6644-4-4-44-44-44-4000000-4-4440040000004-4000000000000000000000000000000000000000000000000
χ674-44-444-4-40004-400000000-44000000000000000000022−22−222222−22−2222000000000000000000000000000000
χ684-44-444-4-40004-400000000-440000000000000000000−222222−22−222222−22000000000000000000000000000000
χ694-44-444-4-4000-44000000004-40000000000022−22−222222−22−222200000000000000000000000000000000000000
χ704-44-444-4-4000-44000000004-400000000000−222222−22−222222−2200000000000000000000000000000000000000
χ714-44-4-4-4440000000004-4-4400000000000002-2-22-222-22-2-22-222-2000000000000000000000000000000
χ724-44-4-4-4440000000004-4-440000000000000-222-22-2-22-222-22-2-22000000000000000000000000000000
χ734-44-4-4-444000000000-444-400000000000002-2-22-222-2-222-22-2-22000000000000000000000000000000
χ744-44-4-4-444000000000-444-40000000000000-222-22-2-222-2-22-222-2000000000000000000000000000000
χ754-4-444-4-44000-4-44-44-4-44-4444000000000000000000000000000000000000000000000000000000000
χ764-4-444-4-44000-4-4-44-444-44-444000000000000000000000000000000000000000000000000000000000
χ774-4-44-444-4000004-4-44000000000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ784-4-44-444-4000004-4-4400000000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ794-4-44-444-400000-444-4000000000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ804-4-44-444-400000-444-400000000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000

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