Finite Group Databasebeta

← Group #351536

Character table — Group #351536

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222224444444444444444444444444444444444444444444444444444444444161616161616161632323232
order12222222444444442244444444444444444444444488888888888888888888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111-11-1
χ91111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ121111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-11
χ17222222222-2-2222-2-222-2-222-2-2000000000000-2-200002222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ18222222222-2-2222-2-222-2-222-2-2000000000000-2-20000-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ19222222222-2-2222-2-2-2-2-2-2-2-2220000000000002200002222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ20222222222-2-2222-2-2-2-2-2-2-2-222000000000000220000-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2122222222-222-2-2-22222-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-200000000000000000000000000000000000000000000
χ2222222222-222-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222200000000000000000000000000000000000000000000
χ2322222222-222-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ2422222222-222-2-2-222-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-200000000000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-222000000000000-2-2000000000000000000002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-222000000000000-2-200000000000000000000−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-200000000000022000000000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-20000000000002200000000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000
χ29222-2-2-22-202-20002-200002i−2i2i−2i00002i2i−2i−2i22-2-200000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ30222-2-2-22-202-20002-200002i−2i2i−2i00002i2i−2i−2i22-2-2000000−2−222−2−222−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ31222-2-2-22-202-20002-200002i−2i2i−2i0000−2i−2i2i2i-2-22200000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ32222-2-2-22-202-20002-200002i−2i2i−2i0000−2i−2i2i2i-2-222000000−2−222−2−222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ33222-2-2-22-202-20002-20000−2i2i−2i2i00002i2i−2i−2i-2-22200000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ34222-2-2-22-202-20002-20000−2i2i−2i2i00002i2i−2i−2i-2-222000000−2−222−2−222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ35222-2-2-22-202-20002-20000−2i2i−2i2i0000−2i−2i2i2i22-2-200000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ36222-2-2-22-202-20002-20000−2i2i−2i2i0000−2i−2i2i2i22-2-2000000−2−222−2−222i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ37222-2-2-22-20-22000-2200002i−2i−2i2i22-2-200000000002i2i−2i−2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i222−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ38222-2-2-22-20-22000-2200002i−2i−2i2i22-2-200000000002i2i−2i−2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ39222-2-2-22-20-22000-2200002i−2i−2i2i-2-2220000000000−2i−2i2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ40222-2-2-22-20-22000-2200002i−2i−2i2i-2-2220000000000−2i−2i2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i222−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ41222-2-2-22-20-22000-220000−2i2i2i−2i22-2-20000000000−2i−2i2i2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i222−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ42222-2-2-22-20-22000-220000−2i2i2i−2i22-2-20000000000−2i−2i2i2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ43222-2-2-22-20-22000-220000−2i2i2i−2i-2-22200000000002i2i−2i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ44222-2-2-22-20-22000-220000−2i2i2i−2i-2-22200000000002i2i−2i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i222−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ452-2-222-22-222-2-2-22-22002-20000000000002i−2i2i−2i002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i2-22-22-22-200000000000000000000
χ462-2-222-22-222-2-2-22-22002-20000000000002i−2i2i−2i002i−2i2i−2i00000000−2i2i−2i2i−2i2i−2i2i-22-22-22-2200000000000000000000
χ472-2-222-22-222-2-2-22-22002-2000000000000−2i2i−2i2i00−2i2i−2i2i000000002i−2i2i−2i2i−2i2i−2i-22-22-22-2200000000000000000000
χ482-2-222-22-222-2-2-22-22002-2000000000000−2i2i−2i2i00−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i2-22-22-22-200000000000000000000
χ492-2-222-22-22-22-2-222-200-2200002i−2i2i−2i2i−2i2i−2i0000000000000000002i−2i2i−2i−2i2i−2i2i000000002-22-22-22-2000000000000
χ502-2-222-22-22-22-2-222-200-2200002i−2i2i−2i2i−2i2i−2i000000000000000000−2i2i−2i2i2i−2i2i−2i00000000-22-22-22-22000000000000
χ512-2-222-22-22-22-2-222-200-220000−2i2i−2i2i−2i2i−2i2i0000000000000000002i−2i2i−2i−2i2i−2i2i00000000-22-22-22-22000000000000
χ522-2-222-22-22-22-2-222-200-220000−2i2i−2i2i−2i2i−2i2i000000000000000000−2i2i−2i2i2i−2i2i−2i000000002-22-22-22-2000000000000
χ532-2-222-22-2-22-222-2-2200-220000000000002i−2i2i−2i00−2i2i−2i2i2-22-22-22-200000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ542-2-222-22-2-22-222-2-2200-220000000000002i−2i2i−2i00−2i2i−2i2i-22-22-22-220000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ552-2-222-22-2-22-222-2-2200-22000000000000−2i2i−2i2i002i−2i2i−2i2-22-22-22-20000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ562-2-222-22-2-22-222-2-2200-22000000000000−2i2i−2i2i002i−2i2i−2i-22-22-22-2200000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ572-2-222-22-2-2-2222-22-2002-200002i−2i2i−2i−2i2i−2i2i00000000002-22-2-22-22000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ582-2-222-22-2-2-2222-22-2002-200002i−2i2i−2i−2i2i−2i2i0000000000-22-222-22-200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ592-2-222-22-2-2-2222-22-2002-20000−2i2i−2i2i2i−2i2i−2i00000000002-22-2-22-2200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ602-2-222-22-2-2-2222-22-2002-20000−2i2i−2i2i2i−2i2i−2i0000000000-22-222-22-2000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ612-2-2-2-2222022000-2-22-20000002i−2i−2i2i00002i−2i−2i2i2-200002−2−222−2−22−222−2−222−2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ622-2-2-2-2222022000-2-22-20000002i−2i−2i2i00002i−2i−2i2i2-20000−222−2−222−22−2−222−2−22−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ632-2-2-2-2222022000-2-22-2000000−2i2i2i−2i0000−2i2i2i−2i2-200002−2−222−2−22−222−2−222−2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ642-2-2-2-2222022000-2-22-2000000−2i2i2i−2i0000−2i2i2i−2i2-20000−222−2−222−22−2−222−2−22i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ652-2-2-2-2222022000-2-2-220000002i−2i−2i2i0000−2i2i2i−2i-2200002−2−222−2−222−2−222−2−22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ662-2-2-2-2222022000-2-2-220000002i−2i−2i2i0000−2i2i2i−2i-220000−222−2−222−2−222−2−222−2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ672-2-2-2-2222022000-2-2-22000000−2i2i2i−2i00002i−2i−2i2i-2200002−2−222−2−222−2−222−2−22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ682-2-2-2-2222022000-2-2-22000000−2i2i2i−2i00002i−2i−2i2i-220000−222−2−222−2−222−2−222−2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ692-2-2-2-22220-2-2000222-200000000002-2-220000-222-2-222−2−22−222−2−222−22−2−22−222−22−2−22−222−2−222−2000000000000
χ702-2-2-2-22220-2-2000222-200000000002-2-220000-222-2-22−222−22−2−222−2−22−222−22−2−22−222−22−2−222−2−22000000000000
χ712-2-2-2-22220-2-2000222-20000000000-222-20000-22-222-22−2−22−222−2−222−22−2−222−2−22−222−22−2−222−2−22000000000000
χ722-2-2-2-22220-2-2000222-20000000000-222-20000-22-222-2−222−22−2−222−2−22−222−2−222−22−2−22−222−2−222−2000000000000
χ732-2-2-2-22220-2-200022-2200000000002-2-2200002-2-222-22−2−22−222−22−2−22−222−2−222−22−2−222−2−222−2−22000000000000
χ742-2-2-2-22220-2-200022-2200000000002-2-2200002-2-222-2−222−22−2−22−222−22−2−222−2−22−222−2−222−2−222−2000000000000
χ752-2-2-2-22220-2-200022-220000000000-222-200002-22-2-222−2−22−222−22−2−22−222−22−2−22−222−2−222−2−222−2000000000000
χ762-2-2-2-22220-2-200022-220000000000-222-200002-22-2-22−222−22−2−22−222−22−2−22−222−22−2−222−2−222−2−22000000000000
χ7744-44-44-4-44004-4-400000000000000000000000000000000000000000000000000000000000022−220000000000
χ7844-44-44-4-44004-4-4000000000000000000000000000000000000000000000000000000000000−22220000000000
χ7944-44-44-4-4-400-444000000000000000000000000000000000000000000000000000000000000002i2−2i200000000
χ8044-44-44-4-4-400-44400000000000000000000000000000000000000000000000000000000000000−2i22i200000000
χ814-444-4-4-44400-44-40000000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ824-444-4-4-44400-44-4000000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ834-444-4-4-44-4004-44000000000000000000000000000000000000000000000000000000000000000022−22000000
χ844-444-4-4-44-4004-440000000000000000000000000000000000000000000000000000000000000000−2222000000
χ8588-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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