Finite Group Databasebeta

← Group #295487

Character table — Group #295487

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444444444444444444444448888888888888888444444444488888888444444888844
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
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1
χ91111111111-1-1-1-1111-1-1-1-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-11-1
χ101111111111-1-1-1-1111-1-1-1-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-111-11
χ111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-111-11
χ121111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-11111-1-1-11
χ141111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1111-1-1-1-1111-1
χ151111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-1-1-11-1-1-111-1-1111-1
χ161111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1111-1-111-1-1-11
χ1722222222222222-2-2-2222222-2-2-2-2-20000-2-20000000000000000000000222200000000-2-20000000000
χ1822222222222222-2-2-2222222-2-2-2-2-20000-2-20000000000000000000000-2-2-2-200000000220000000000
χ192222222222-2-2-2-2-2-2-2-2-2-2-222-222220000-2-2000000000000000000000022-2-200000000-220000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-222-222220000-2-20000000000000000000000-2-222000000002-20000000000
χ2122222222-2-22222222-2-2-2-2-2-2222-2-22222-2-20000000000000000-2-222-2-2000000000000000000000000
χ2222222222-2-22222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-2000000000000000022-2-222000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2220000220000000000000000000000000000000000002-22-2000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222000022000000000000000000000000000000000000-22-22000000
χ2522222222-2-2-2-2-2-22222222-2-22-2-2222222-2-20000000000000000-2-2-2-222000000000000000000000000
χ2622222222-2-2-2-2-2-22222222-2-22-2-222-2-2-2-2-2-200000000000000002222-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-222-2-20000220000000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-222-2-2000022000000000000000000000000000000000000-222-2000000
χ29222-2-2-2-22-2-222-2-200022-2-22200000000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000002-22-200000000000000i2−i2i2−i200
χ30222-2-2-2-22-2-222-2-200022-2-22200000000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000-22-2200000000000000−i2i2−i2i200
χ31222-2-2-2-22-2-222-2-200022-2-22200000000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000002-22-200000000000000−i2i2−i2i200
χ32222-2-2-2-22-2-222-2-200022-2-22200000000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2000000-22-2200000000000000i2−i2i2−i200
χ33222-2-2-2-22-2-2-2-222000-2-2222200000000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000002-2-2200000000000000i2−i2−i2i200
χ34222-2-2-2-22-2-2-2-222000-2-2222200000000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2000000-222-200000000000000−i2i2i2−i200
χ35222-2-2-2-22-2-2-2-222000-2-2222200000000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000002-2-2200000000000000−i2i2i2−i200
χ36222-2-2-2-22-2-2-2-222000-2-2222200000000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2000000-222-200000000000000i2−i2−i2i200
χ3722-22-2-22-2002-22-22-2-200000022-2002i2i−2i−2i00i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i00000022−2−222−2−2000000000000
χ3822-22-2-22-2002-22-22-2-200000022-2002i2i−2i−2i00−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i000000−2−222−2−222000000000000
χ3922-22-2-22-2002-22-22-2-200000022-200−2i−2i2i2i00i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i000000−2−222−2−222000000000000
χ4022-22-2-22-2002-22-22-2-200000022-200−2i−2i2i2i00−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00000022−2−222−2−2000000000000
χ4122-22-2-22-200-22-222-2-20000002-22002i2i−2i−2i00i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200−2i2i00000022−2−2−2−222000000000000
χ4222-22-2-22-200-22-222-2-20000002-22002i2i−2i−2i00−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200−2i2i000000−2−22222−2−2000000000000
χ4322-22-2-22-200-22-222-2-20000002-2200−2i−2i2i2i00i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002i−2i000000−2−22222−2−2000000000000
χ4422-22-2-22-200-22-222-2-20000002-2200−2i−2i2i2i00−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002i−2i00000022−2−2−2−222000000000000
χ452-22-22-22-22-20000-22-200002-2200002i−2i2i−2i2-2000000002i−2i2i−2i2i−2i2i−2i2i−2i0000000000002-22-2000000000000
χ462-22-22-22-22-20000-22-200002-2200002i−2i2i−2i2-200000000−2i2i−2i2i−2i2i−2i2i2i−2i000000000000-22-22000000000000
χ472-22-22-22-22-20000-22-200002-220000−2i2i−2i2i2-2000000002i−2i2i−2i2i−2i2i−2i−2i2i000000000000-22-22000000000000
χ482-22-22-22-22-20000-22-200002-220000−2i2i−2i2i2-200000000−2i2i−2i2i−2i2i−2i2i−2i2i0000000000002-22-2000000000000
χ492-22-22-22-2-220000-22-20000-22200002i−2i2i−2i-222i−2i2i−2i2i−2i2i−2i00000000−2i2i000000002-22-20000000000000000
χ502-22-22-22-2-220000-22-20000-22200002i−2i2i−2i-22−2i2i−2i2i−2i2i−2i2i00000000−2i2i00000000-22-220000000000000000
χ512-22-22-22-2-220000-22-20000-2220000−2i2i−2i2i-222i−2i2i−2i2i−2i2i−2i000000002i−2i00000000-22-220000000000000000
χ522-22-22-22-2-220000-22-20000-2220000−2i2i−2i2i-22−2i2i−2i2i−2i2i−2i2i000000002i−2i000000002-22-20000000000000000
χ532-2-2-2-2222000000-2-222-22-2002002-22-2-22002−2−222−2−222−2−222−2−2200002-200002−2−222−2−22000000000000
χ542-2-2-2-2222000000-2-222-22-2002002-22-2-2200−222−2−222−2−222−2−222−200002-20000−222−2−222−2000000000000
χ552-2-2-2-2222000000-2-222-22-2002002-2-222-2002−2−222−2−222−2−222−2−220000-220000−222−2−222−2000000000000
χ562-2-2-2-2222000000-2-222-22-2002002-2-222-200−222−2−222−2−222−2−222−20000-2200002−2−222−2−22000000000000
χ572-2-2-2-2222000000-2-22-22-2200200-222-2-22002−2−222−2−22−222−2−222−20000-2200002−2−22−222−2000000000000
χ582-2-2-2-2222000000-2-22-22-2200200-222-2-2200−222−2−222−22−2−222−2−220000-220000−222−22−2−22000000000000
χ592-2-2-2-2222000000-2-22-22-2200200-22-222-2002−2−222−2−22−222−2−222−200002-20000−222−22−2−22000000000000
χ602-2-2-2-2222000000-2-22-22-2200200-22-222-200−222−2−222−22−2−222−2−2200002-200002−2−22−222−2000000000000
χ61444-4-4-4-444444-4-4000-4-444-4-4000000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-4444-4-44400044-4-4-4-4000000000000000000000000000000000000000000000000000000000
χ6344-44-4-44-4004-44-4-444000000-4-44000000000000000000000000000000000000000000000000000000
χ6444-44-4-44-400-44-44-444000000-44-4000000000000000000000000000000000000000000000000000000
χ6544-4-444-4-4004-4-440000000000000000000022-2-2-2-22222-2-2-2-222000000000000000000000000000000
χ6644-4-444-4-4004-4-4400000000000000000000-2-22222-2-2-2-22222-2-2000000000000000000000000000000
χ6744-4-444-4-400-444-40000000000000000000022-2-2-2-222-2-22222-2-2000000000000000000000000000000
χ6844-4-444-4-400-444-400000000000000000000-2-22222-2-222-2-2-2-222000000000000000000000000000000
χ694-444-44-4-44-400000000000-440000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ704-444-44-4-44-400000000000-4400000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ714-444-44-4-4-44000000000004-4000000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ724-444-44-4-4-44000000000004-40000000000000000000−2222−222222−2222−22000000000000000000000000000000
χ734-44-44-44-44-400004-4400004-4-400000000-440000000000000000000000000000000000000000000000
χ744-44-44-44-4-4400004-440000-44-4000000004-40000000000000000000000000000000000000000000000
χ754-4-444-4-440000000004-4-4400000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ764-4-444-4-440000000004-4-440000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ774-4-444-4-44000000000-444-400000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ784-4-444-4-44000000000-444-40000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ794-4-4-4-444400000044-44-44-400-400-440000000000000000000000000000000000000000000000000000
χ804-4-4-4-444400000044-4-44-4400-4004-40000000000000000000000000000000000000000000000000000

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