Finite Group Databasebeta

← Group #351546

Character table — Group #351546

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222224444444444444444444444444444444444444444444444444444444444161616161616161632323232
order12222222444444442244444444444444444444444488888888888888888888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1
χ91111111111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ121111111111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-11
χ17222222222222-2-2-2-222-2-222-2-222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ18222222222222-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2222200000000000000000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-200000000000000000000000000000000000000000000
χ2122222222-2-2-2-2222222-2-2-2-2-2-20000000022000000002222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2222222222-2-2-2-2222222-2-2-2-2-2-2000000002200000000-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2322222222-2-2-2-22222-2-2-2-2222200000000-2-2000000002222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-2222200000000-2-200000000-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-22200000000-2-20000000000000000000000002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-22200000000-2-2000000000000000000000000−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-200000000220000000000000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-20000000022000000000000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000
χ29222-2-2-2-2222-2-200000000002i−2i00002i2i−2i−2i2i−2i22-2-20000i2i2−i2−i2i2i2−i2−i222−2−222−2−2i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ30222-2-2-2-2222-2-200000000002i−2i00002i2i−2i−2i2i−2i22-2-20000−i2−i2i2i2−i2−i2i2i2−2−222−2−222−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ31222-2-2-2-2222-2-200000000002i−2i0000−2i−2i2i2i2i−2i-2-2220000i2i2−i2−i2i2i2−i2−i222−2−222−2−2−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ32222-2-2-2-2222-2-200000000002i−2i0000−2i−2i2i2i2i−2i-2-2220000−i2−i2i2i2−i2−i2i2i2−2−222−2−222i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ33222-2-2-2-2222-2-20000000000−2i2i00002i2i−2i−2i−2i2i-2-2220000i2i2−i2−i2i2i2−i2−i2−2−222−2−222−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ34222-2-2-2-2222-2-20000000000−2i2i00002i2i−2i−2i−2i2i-2-2220000−i2−i2i2i2−i2−i2i2i222−2−222−2−2i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ35222-2-2-2-2222-2-20000000000−2i2i0000−2i−2i2i2i−2i2i22-2-20000i2i2−i2−i2i2i2−i2−i2−2−222−2−222i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ36222-2-2-2-2222-2-20000000000−2i2i0000−2i−2i2i2i−2i2i22-2-20000−i2−i2i2i2−i2−i2i2i222−2−222−2−2−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ37222-2-2-2-22-2-22200000000002i−2i2i2i−2i−2i0000−2i2i000022-2-2i2i2−i2−i2−i2−i2i2i2−2−22222−2−222−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ38222-2-2-2-22-2-22200000000002i−2i2i2i−2i−2i0000−2i2i000022-2-2−i2−i2i2i2i2i2−i2−i222−2−2−2−222−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ39222-2-2-2-22-2-22200000000002i−2i−2i−2i2i2i0000−2i2i0000-2-222i2i2−i2−i2−i2−i2i2i2−2−22222−2−2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ40222-2-2-2-22-2-22200000000002i−2i−2i−2i2i2i0000−2i2i0000-2-222−i2−i2i2i2i2i2−i2−i222−2−2−2−22222−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ41222-2-2-2-22-2-2220000000000−2i2i2i2i−2i−2i00002i−2i0000-2-222i2i2−i2−i2−i2−i2i2i222−2−2−2−22222−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ42222-2-2-2-22-2-2220000000000−2i2i2i2i−2i−2i00002i−2i0000-2-222−i2−i2i2i2i2i2−i2−i2−2−22222−2−2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ43222-2-2-2-22-2-2220000000000−2i2i−2i−2i2i2i00002i−2i000022-2-2i2i2−i2−i2−i2−i2i2i222−2−2−2−222−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ44222-2-2-2-22-2-2220000000000−2i2i−2i−2i2i2i00002i−2i000022-2-2−i2−i2i2i2i2i2−i2−i2−2−22222−2−222−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ452-222-2-22-22-22-222-2-2002-2000000002i−2i2i−2i0000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i2-22-22-22-200000000000000000000
χ462-222-2-22-22-22-222-2-2002-2000000002i−2i2i−2i0000002i−2i2i−2i00000000−2i2i−2i2i−2i2i−2i2i-22-22-22-2200000000000000000000
χ472-222-2-22-22-22-222-2-2002-200000000−2i2i−2i2i000000−2i2i−2i2i000000002i−2i2i−2i2i−2i2i−2i-22-22-22-2200000000000000000000
χ482-222-2-22-22-22-222-2-2002-200000000−2i2i−2i2i000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i2-22-22-22-200000000000000000000
χ492-222-2-22-22-22-2-2-22200-22000000002i−2i2i−2i000000−2i2i−2i2i2-22-22-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ502-222-2-22-22-22-2-2-22200-22000000002i−2i2i−2i000000−2i2i−2i2i-22-22-22-220000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ512-222-2-22-22-22-2-2-22200-2200000000−2i2i−2i2i0000002i−2i2i−2i2-22-22-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ522-222-2-22-22-22-2-2-22200-2200000000−2i2i−2i2i0000002i−2i2i−2i-22-22-22-2200000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ532-222-2-22-2-22-2222-2-200-2200002i−2i2i−2i0000002i−2i2i−2i0000000000002i−2i2i−2i−2i2i−2i2i000000002-22-2-22-22000000000000
χ542-222-2-22-2-22-2222-2-200-2200002i−2i2i−2i0000002i−2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i00000000-22-222-22-2000000000000
χ552-222-2-22-2-22-2222-2-200-220000−2i2i−2i2i000000−2i2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i00000000-22-222-22-2000000000000
χ562-222-2-22-2-22-2222-2-200-220000−2i2i−2i2i000000−2i2i−2i2i000000000000−2i2i−2i2i2i−2i2i−2i000000002-22-2-22-22000000000000
χ572-222-2-22-2-22-22-2-222002-200002i−2i2i−2i000000−2i2i−2i2i00002-22-2-22-22000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ582-222-2-22-2-22-22-2-222002-200002i−2i2i−2i000000−2i2i−2i2i0000-22-222-22-200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ592-222-2-22-2-22-22-2-222002-20000−2i2i−2i2i0000002i−2i2i−2i00002-22-2-22-2200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ602-222-2-22-2-22-22-2-222002-20000−2i2i−2i2i0000002i−2i2i−2i0000-22-222-22-2000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ612-22-222-2-22-2-2200002-2002-2002-2-222-2-220000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ622-22-222-2-22-2-2200002-2002-2002-2-222-2-220000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ632-22-222-2-22-2-2200002-2002-200-222-2-222-20000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ642-22-222-2-22-2-2200002-2002-200-222-2-222-20000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ652-22-222-2-22-2-220000-2200-22002-2-22-222-20000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ662-22-222-2-22-2-220000-2200-22002-2-22-222-20000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ672-22-222-2-22-2-220000-2200-2200-222-22-2-220000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ682-22-222-2-22-2-220000-2200-2200-222-22-2-220000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ692-22-222-2-2-222-200002-200-220000000000002i−2i−2i2i−2i2i2i−2ii2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i22−2−22−222−22−2−22−222−2000000000000
χ702-22-222-2-2-222-200002-200-220000000000002i−2i−2i2i−2i2i2i−2i−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−222−22−2−22−222−22−2−22000000000000
χ712-22-222-2-2-222-200002-200-22000000000000−2i2i2i−2i2i−2i−2i2ii2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−222−22−2−22−222−22−2−22000000000000
χ722-22-222-2-2-222-200002-200-22000000000000−2i2i2i−2i2i−2i−2i2i−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i22−2−22−222−22−2−22−222−2000000000000
χ732-22-222-2-2-222-20000-22002-20000000000002i−2i−2i2i2i−2i−2i2ii2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i22−2−22−222−2−222−22−2−22000000000000
χ742-22-222-2-2-222-20000-22002-20000000000002i−2i−2i2i2i−2i−2i2i−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−222−22−2−222−2−22−222−2000000000000
χ752-22-222-2-2-222-20000-22002-2000000000000−2i2i2i−2i−2i2i2i−2ii2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−222−22−2−222−2−22−222−2000000000000
χ762-22-222-2-2-222-20000-22002-2000000000000−2i2i2i−2i−2i2i2i−2i−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i22−2−22−222−2−222−22−2−22000000000000
χ7744-4-44-44-400004-44-40000000000000000000000000000000000000000000000000000000000002i2−2i200000000
χ7844-4-44-44-400004-44-4000000000000000000000000000000000000000000000000000000000000−2i22i200000000
χ7944-4-44-44-40000-44-4400000000000000000000000000000000000000000000000000000000002i2−2i20000000000
χ8044-4-44-44-40000-44-440000000000000000000000000000000000000000000000000000000000−2i22i20000000000
χ814-4-4-4-444400004-4-440000000000000000000000000000000000000000000000000000000000000022−22000000
χ824-4-4-4-444400004-4-4400000000000000000000000000000000000000000000000000000000000000−2222000000
χ834-4-4-4-44440000-444-4000000000000000000000000000000000000000000000000000000000000000022−220000
χ844-4-4-4-44440000-444-40000000000000000000000000000000000000000000000000000000000000000−22220000
χ8588-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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