Finite Group Databasebeta

← Group #351537

Character table — Group #351537

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222224444444444444444444444444444444444444444444444444444444444161616161616161632323232
order12222222444444442244444444444444444444444488888888888888888888888888888888888888884444
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
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-11-11
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111-11-1
χ91111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ121111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-11
χ172222222222-2-2-222-222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ182222222222-2-2-222-22222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2-2-222222222-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2000000000000-2-222-2-200002222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2222222222-2-2222-2-2222-2-2000000000000-2-222-2-20000-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2322222222-2-2222-2-22-2-222000000000000-2-2-2-22200002222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-2222-2-22-2-222000000000000-2-2-2-2220000-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-200000000000022-2-222000000000000000000002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-200000000000022-2-22200000000000000000000−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2220000000000002222-2-2000000000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2220000000000002222-2-200000000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000
χ292222-2-2-2-222000-2-202-22-222-2-2000022-2-2000000000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2000000000000
χ302222-2-2-2-222000-2-202-22-222-2-2000022-2-20000000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−222000000000000
χ312222-2-2-2-222000-2-202-22-2-2-2220000-2-222000000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−222000000000000
χ322222-2-2-2-222000-2-202-22-2-2-2220000-2-2220000000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−2000000000000
χ332222-2-2-2-222000-2-20-22-2222-2-20000-2-222000000000022−2−222−2−2−2−222−2−22222−2−222−2−2−2−222−2−222000000000000
χ342222-2-2-2-222000-2-20-22-2222-2-20000-2-2220000000000−2−222−2−22222−2−222−2−2−2−222−2−22222−2−222−2−2000000000000
χ352222-2-2-2-222000-2-20-22-22-2-222000022-2-2000000000022−2−222−2−2−2−222−2−222−2−222−2−22222−2−222−2−2000000000000
χ362222-2-2-2-222000-2-20-22-22-2-222000022-2-20000000000−2−222−2−22222−2−222−2−222−2−222−2−2−2−222−2−222000000000000
χ372222-2-2-2-2-2-20002202-2-2200002i2i−2i−2i00000000002i2i−2i−2i22−2−2−2−22222−2−2−2−222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ382222-2-2-2-2-2-20002202-2-2200002i2i−2i−2i00000000002i2i−2i−2i−2−22222−2−2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ392222-2-2-2-2-2-20002202-2-220000−2i−2i2i2i0000000000−2i−2i2i2i22−2−2−2−22222−2−2−2−222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ402222-2-2-2-2-2-20002202-2-220000−2i−2i2i2i0000000000−2i−2i2i2i−2−22222−2−2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ412222-2-2-2-2-2-2000220-222-200002i2i−2i−2i0000000000−2i−2i2i2i22−2−2−2−222−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ422222-2-2-2-2-2-2000220-222-200002i2i−2i−2i0000000000−2i−2i2i2i−2−22222−2−222−2−2−2−222−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ432222-2-2-2-2-2-2000220-222-20000−2i−2i2i2i00000000002i2i−2i−2i22−2−2−2−222−2−22222−2−2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ442222-2-2-2-2-2-2000220-222-20000−2i−2i2i2i00000000002i2i−2i−2i−2−22222−2−222−2−2−2−222i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ4522-2-22-2-222-20002-20000000002-22-22i−2i2i−2i002i−2i2i−2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ4622-2-22-2-222-20002-20000000002-22-22i−2i2i−2i002i−2i2i−2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ4722-2-22-2-222-20002-20000000002-22-2−2i2i−2i2i00−2i2i−2i2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ4822-2-22-2-222-20002-20000000002-22-2−2i2i−2i2i00−2i2i−2i2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ4922-2-22-2-222-20002-2000000000-22-222i−2i2i−2i00−2i2i−2i2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i2−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ5022-2-22-2-222-20002-2000000000-22-222i−2i2i−2i00−2i2i−2i2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i22−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ5122-2-22-2-222-20002-2000000000-22-22−2i2i−2i2i002i−2i2i−2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i2−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ5222-2-22-2-222-20002-2000000000-22-22−2i2i−2i2i002i−2i2i−2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i22−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ5322-2-22-2-22-22000-22000002i−2i2i−2i00000000002i−2i−2i2i2-22-22−22−2−22−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ5422-2-22-2-22-22000-22000002i−2i2i−2i00000000002i−2i−2i2i2-22-2−22−222−22−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ5522-2-22-2-22-22000-22000002i−2i2i−2i0000000000−2i2i2i−2i-22-222−22−2−22−22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ5622-2-22-2-22-22000-22000002i−2i2i−2i0000000000−2i2i2i−2i-22-22−22−222−22−2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ5722-2-22-2-22-22000-2200000−2i2i−2i2i00000000002i−2i−2i2i-22-222−22−2−22−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ5822-2-22-2-22-22000-2200000−2i2i−2i2i00000000002i−2i−2i2i-22-22−22−222−22−2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ5922-2-22-2-22-22000-2200000−2i2i−2i2i0000000000−2i2i2i−2i2-22-22−22−2−22−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ6022-2-22-2-22-22000-2200000−2i2i−2i2i0000000000−2i2i2i−2i2-22-2−22−222−22−2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ6122-2-2-222-22-22-2-2-2220000000000002i−2i−2i2i2-20000−2i2i2i−2i000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-2200000000000000000000
χ6222-2-2-222-22-22-2-2-2220000000000002i−2i−2i2i2-20000−2i2i2i−2i00000000−2i2i2i−2i−2i2i2i−2i-222-2-222-200000000000000000000
χ6322-2-2-222-22-22-2-2-222000000000000−2i2i2i−2i2-200002i−2i−2i2i000000002i−2i−2i2i2i−2i−2i2i-222-2-222-200000000000000000000
χ6422-2-2-222-22-22-2-2-222000000000000−2i2i2i−2i2-200002i−2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-2200000000000000000000
χ6522-2-2-222-22-2-222-22-20000000000002i−2i−2i2i-2200002i−2i−2i2i2-2-222-2-2200000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ6622-2-2-222-22-2-222-22-20000000000002i−2i−2i2i-2200002i−2i−2i2i-222-2-222-20000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ6722-2-2-222-22-2-222-22-2000000000000−2i2i2i−2i-220000−2i2i2i−2i2-2-222-2-220000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ6822-2-2-222-22-2-222-22-2000000000000−2i2i2i−2i-220000−2i2i2i−2i-222-2-222-200000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ6922-2-2-222-2-222-2-22-2200002i−2i−2i2i−2i2i2i−2i0000-2200000000000000002i−2i−2i2i−2i2i2i−2i000000002-2-22-222-2000000000000
χ7022-2-2-222-2-222-2-22-2200002i−2i−2i2i−2i2i2i−2i0000-220000000000000000−2i2i2i−2i2i−2i−2i2i00000000-222-22-2-22000000000000
χ7122-2-2-222-2-222-2-22-220000−2i2i2i−2i2i−2i−2i2i0000-2200000000000000002i−2i−2i2i−2i2i2i−2i00000000-222-22-2-22000000000000
χ7222-2-2-222-2-222-2-22-220000−2i2i2i−2i2i−2i−2i2i0000-220000000000000000−2i2i2i−2i2i−2i−2i2i000000002-2-22-222-2000000000000
χ7322-2-2-222-2-22-2222-2-200002i−2i−2i2i2i−2i−2i2i00002-2000000002-2-22-222-2000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ7422-2-2-222-2-22-2222-2-200002i−2i−2i2i2i−2i−2i2i00002-200000000-222-22-2-2200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ7522-2-2-222-2-22-2222-2-20000−2i2i2i−2i−2i2i2i−2i00002-2000000002-2-22-222-200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ7622-2-2-222-2-22-2222-2-20000−2i2i2i−2i−2i2i2i−2i00002-200000000-222-22-2-22000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ774-44-444-4-40044-400-40000000000000000000000000000000000000000000000000000000000000022−22000000
χ784-44-444-4-40044-400-400000000000000000000000000000000000000000000000000000000000000−2222000000
χ794-44-444-4-400-4-4400400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ804-44-444-4-400-4-440040000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ814-4-44-44-44004-4400-40000000000000000000000000000000000000000000000000000000000002i2−2i200000000
χ824-4-44-44-44004-4400-4000000000000000000000000000000000000000000000000000000000000−2i22i200000000
χ834-4-44-44-4400-44-4004000000000000000000000000000000000000000000000000000000000022−220000000000
χ844-4-44-44-4400-44-40040000000000000000000000000000000000000000000000000000000000−22220000000000
χ858-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-888-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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