Finite Group Databasebeta

← Group #225752

Character table — Group #225752

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12224444224444448888888888888888222244444488888888888888888888888822448888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11-1-1-1-11111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1111-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1111-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-11-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ171111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11ii−i−iii−i−i11-1-111-1-11111-1-1-1-1-1-111i−ii−iii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i
χ181111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11−i−iii−i−iii11-1-111-1-11111-1-1-1-1-1-111−ii−ii−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii
χ191111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-111111ii−i−iii−i−i11-1-111-1-11111-1-1-1-111-1-1i−ii−iii−i−iii−i−i-1-111-1-111−ii−ii−ii−ii
χ201111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-111111−i−iii−i−iii11-1-111-1-11111-1-1-1-111-1-1−ii−ii−i−iii−i−iii-1-111-1-111i−ii−ii−ii−i
χ211111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11ii−i−i−i−iii11-1-1-1-111-1-1-1-11111-1-111i−i−iiii−i−i−i−iii-1-111-1-111i−ii−i−ii−ii
χ221111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11−i−iiiii−i−i11-1-1-1-111-1-1-1-11111-1-111−iii−i−i−iiiii−i−i-1-111-1-111−ii−iii−ii−i
χ231111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-111111ii−i−i−i−iii11-1-1-1-111-1-1-1-1111111-1-1i−i−iiii−i−i−i−iii11-1-111-1-1−ii−iii−ii−i
χ241111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-111111−i−iiiii−i−i11-1-1-1-111-1-1-1-1111111-1-1−iii−i−i−iiiii−i−i11-1-111-1-1i−ii−i−ii−ii
χ251111-1-1-1-1-1-1111-1-11-1-1-1-111111111-1-1-1-111-1-1-1-1-1111ii−i−iii−i−i-1-11111-1-1-1-1-1-11111-111-1i−ii−i−i−iii−i−iii11-1-1-1-111i−i−iii−i−ii
χ261111-1-1-1-1-1-1111-1-11-1-1-1-111111111-1-1-1-111-1-1-1-1-1111−i−iii−i−iii-1-11111-1-1-1-1-1-11111-111-1−ii−iiii−i−iii−i−i11-1-1-1-111−iii−i−iii−i
χ271111-1-1-1-1-1-1111-1-11-1-1-1-111111111-1-1-1-1-1-111-111-1-11ii−i−iii−i−i-1-11111-1-1-1-1-1-111111-1-11i−ii−i−i−iii−i−iii-1-11111-1-1−iii−i−iii−i
χ281111-1-1-1-1-1-1111-1-11-1-1-1-111111111-1-1-1-1-1-111-111-1-11−i−iii−i−iii-1-11111-1-1-1-1-1-111111-1-11−ii−iiii−i−iii−i−i-1-11111-1-1i−i−iii−i−ii
χ291111-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-1-1111111-1-1-1-1-1111ii−i−i−i−iii-1-111-1-1111111-1-1-1-1-111-1i−i−ii−i−iiiii−i−i-1-11111-1-1i−i−ii−iii−i
χ301111-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-1-1111111-1-1-1-1-1111−i−iiiii−i−i-1-111-1-1111111-1-1-1-1-111-1−iii−iii−i−i−i−iii-1-11111-1-1−iii−ii−i−ii
χ311111-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-1-11111-1-111-111-1-11ii−i−i−i−iii-1-111-1-1111111-1-1-1-11-1-11i−i−ii−i−iiiii−i−i11-1-1-1-111−iii−ii−i−ii
χ321111-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-1-11111-1-111-111-1-11−i−iiiii−i−i-1-111-1-1111111-1-1-1-11-1-11−iii−iii−i−i−i−iii11-1-1-1-111i−i−ii−iii−i
χ332222222222-2-22-2-2200000000222222220000-20000-2222222220000-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ342222222222-2-22-2-2200000000222222220000-20000-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000002222000000000000000000000000
χ352222222222-2-22-2-2200000000-2-2-2-2-2-2-2-20000-20000-22222-2-2-2-200002222000000000000-2-222000000000000000000000000
χ362222222222-2-22-2-2200000000-2-2-2-2-2-2-2-20000-20000-2-2-2-2-222220000222200000000000022-2-2000000000000000000000000
χ3722222222-2-222-222-222222222000000002222-22222-200000000-2-2-2-2000000000000-2-2-2-20000000000000000000000000000
χ3822222222-2-222-222-22222222200000000-2-2-2-2-2-2-2-2-2-200000000-2-2-2-200000000000022220000000000000000000000000000
χ3922222222-2-222-222-2-2-2-2-2-2-2-2-20000000022-2-2-222-2-2-2000000002222000000000000-22-220000000000000000000000000000
χ4022222222-2-222-222-2-2-2-2-2-2-2-2-200000000-2-222-2-2-222-20000000022220000000000002-22-20000000000000000000000000000
χ412222-2-2-2-22222-2-2-2-22222-2-2-2-20000000022222-2-2-2-2-200000000-2-22200000000000022-2-20000000000000000000000000000
χ422222-2-2-2-22222-2-2-2-22222-2-2-2-200000000-2-2-2-222222-200000000-2-222000000000000-2-2220000000000000000000000000000
χ432222-2-2-2-22222-2-2-2-2-2-2-2-222220000000022-2-22-2-222-20000000022-2-20000000000002-2-220000000000000000000000000000
χ442222-2-2-2-22222-2-2-2-2-2-2-2-2222200000000-2-222222-2-2-20000000022-2-2000000000000-222-20000000000000000000000000000
χ452222-2-2-2-2-2-2-2-22222000000002222-2-2-2-2000020000-22i2i−2i−2i2i2i−2i−2i0000-2-222000000000000−2i2i−2i2i000000000000000000000000
χ462222-2-2-2-2-2-2-2-22222000000002222-2-2-2-2000020000-2−2i−2i2i2i−2i−2i2i2i0000-2-2220000000000002i−2i2i−2i000000000000000000000000
χ472222-2-2-2-2-2-2-2-2222200000000-2-2-2-22222000020000-22i2i−2i−2i−2i−2i2i2i000022-2-2000000000000−2i2i2i−2i000000000000000000000000
χ482222-2-2-2-2-2-2-2-2222200000000-2-2-2-22222000020000-2−2i−2i2i2i2i2i−2i−2i000022-2-20000000000002i−2i−2i2i000000000000000000000000
χ4922-2-22i2i−2i−2i002-202i−2i022-2-22i2i−2i−2ii2i2−i2−i222−2−22-22-202i−2i2i−2i0000000000000i2−i22−2i2i2−i2−i222−2−20000000000000000i2−i22−2i2−i22−200000000
χ5022-2-22i2i−2i−2i002-202i−2i022-2-22i2i−2i−2ii2i2−i2−i222−2−2-22-220−2i2i−2i2i0000000000000i2−i22−2i2i2−i2−i222−2−20000000000000000−i2i2−22−i2i2−2200000000
χ5122-2-22i2i−2i−2i002-202i−2i022-2-22i2i−2i−2i−i2−i2i2i2−2−2222-22-202i−2i2i−2i0000000000000−i2i2−22−i2−i2i2i2−2−2220000000000000000−i2i2−22−i2i2−2200000000
χ5222-2-22i2i−2i−2i002-202i−2i022-2-22i2i−2i−2i−i2−i2i2i2−2−222-22-220−2i2i−2i2i0000000000000−i2i2−22−i2−i2i2i2−2−2220000000000000000i2−i22−2i2−i22−200000000
χ5322-2-22i2i−2i−2i002-202i−2i0-2-222−2i−2i2i2ii2i2−i2−i222−2−22-2-2202i−2i−2i2i0000000000000i2−i22−2−i2−i2i2i2−2−2220000000000000000i2−i22−2−i2i2−2200000000
χ5422-2-22i2i−2i−2i002-202i−2i0-2-222−2i−2i2i2ii2i2−i2−i222−2−2-222-20−2i2i2i−2i0000000000000i2−i22−2−i2−i2i2i2−2−2220000000000000000−i2i2−22i2−i22−200000000
χ5522-2-22i2i−2i−2i002-202i−2i0-2-222−2i−2i2i2i−i2−i2i2i2−2−2222-2-2202i−2i−2i2i0000000000000−i2i2−22i2i2−i2−i222−2−20000000000000000−i2i2−22i2−i22−200000000
χ5622-2-22i2i−2i−2i002-202i−2i0-2-222−2i−2i2i2i−i2−i2i2i2−2−222-222-20−2i2i2i−2i0000000000000−i2i2−22i2i2−i2−i222−2−20000000000000000i2−i22−2−i2i2−2200000000
χ5722-2-2−2i−2i2i2i002-20−2i2i022-2-2−2i−2i2i2ii2i2−i2−i2−2−2222-22-20−2i2i−2i2i0000000000000i2−i2−22i2i2−i2−i2−2−2220000000000000000i2−i2−22i2−i2−2200000000
χ5822-2-2−2i−2i2i2i002-20−2i2i022-2-2−2i−2i2i2ii2i2−i2−i2−2−222-22-2202i−2i2i−2i0000000000000i2−i2−22i2i2−i2−i2−2−2220000000000000000−i2i22−2−i2i22−200000000
χ5922-2-2−2i−2i2i2i002-20−2i2i022-2-2−2i−2i2i2i−i2−i2i2i222−2−22-22-20−2i2i−2i2i0000000000000−i2i22−2−i2−i2i2i222−2−20000000000000000−i2i22−2−i2i22−200000000
χ6022-2-2−2i−2i2i2i002-20−2i2i022-2-2−2i−2i2i2i−i2−i2i2i222−2−2-22-2202i−2i2i−2i0000000000000−i2i22−2−i2−i2i2i222−2−20000000000000000i2−i2−22i2−i2−2200000000
χ6122-2-2−2i−2i2i2i002-20−2i2i0-2-2222i2i−2i−2ii2i2−i2−i2−2−2222-2-220−2i2i2i−2i0000000000000i2−i2−22−i2−i2i2i222−2−20000000000000000i2−i2−22−i2i22−200000000
χ6222-2-2−2i−2i2i2i002-20−2i2i0-2-2222i2i−2i−2ii2i2−i2−i2−2−222-222-202i−2i−2i2i0000000000000i2−i2−22−i2−i2i2i222−2−20000000000000000−i2i22−2i2−i2−2200000000
χ6322-2-2−2i−2i2i2i002-20−2i2i0-2-2222i2i−2i−2i−i2−i2i2i222−2−22-2-220−2i2i2i−2i0000000000000−i2i22−2i2i2−i2−i2−2−2220000000000000000−i2i22−2i2−i2−2200000000
χ6422-2-2−2i−2i2i2i002-20−2i2i0-2-2222i2i−2i−2i−i2−i2i2i222−2−2-222-202i−2i−2i2i0000000000000−i2i22−2i2i2−i2−i2−2−2220000000000000000i2−i2−22−i2i22−200000000
χ652-2-222-22-22-200200-22−22−22−22−22i−2i2i−2i2i−2i2i−2i00000000002-22-22i−2i2i−2i2−22−20000i2−i2i2−i2i2−i2i2−i2000000002−22−2i2−i2i2−i20000000000000000
χ662-2-222-22-22-200200-22−22−22−22−22i−2i2i−2i2i−2i2i−2i0000000000-22-22−2i2i−2i2i2−22−20000i2−i2i2−i2i2−i2i2−i200000000−22−22−i2i2−i2i20000000000000000
χ672-2-222-22-22-200200-22−22−22−22−2−2i2i−2i2i−2i2i−2i2i00000000002-22-2−2i2i−2i2i2−22−20000−i2i2−i2i2−i2i2−i2i2000000002−22−2−i2i2−i2i20000000000000000
χ682-2-222-22-22-200200-22−22−22−22−2−2i2i−2i2i−2i2i−2i2i0000000000-22-222i−2i2i−2i2−22−20000−i2i2−i2i2−i2i2−i2i200000000−22−22i2−i2i2−i20000000000000000
χ692-2-222-22-22-200200-2−22−22−22−222i−2i2i−2i2i−2i2i−2i00000000002-22-22i−2i2i−2i−22−220000−i2i2−i2i2−i2i2−i2i200000000−22−22−i2i2−i2i20000000000000000
χ702-2-222-22-22-200200-2−22−22−22−222i−2i2i−2i2i−2i2i−2i0000000000-22-22−2i2i−2i2i−22−220000−i2i2−i2i2−i2i2−i2i2000000002−22−2i2−i2i2−i20000000000000000
χ712-2-222-22-22-200200-2−22−22−22−22−2i2i−2i2i−2i2i−2i2i00000000002-22-2−2i2i−2i2i−22−220000i2−i2i2−i2i2−i2i2−i200000000−22−22i2−i2i2−i20000000000000000
χ722-2-222-22-22-200200-2−22−22−22−22−2i2i−2i2i−2i2i−2i2i0000000000-22-222i−2i2i−2i−22−220000i2−i2i2−i2i2−i2i2−i2000000002−22−2−i2i2−i2i20000000000000000
χ732-2-22-22-22-2200200-22−22−2−22−222i−2i2i−2i−2i2i−2i2i00000000002i−2i−2i2i-222-22−2−220000i2−i2i2−i2−i2i2−i2i200000000i2−i2−i2i2−222−20000000000000000
χ742-2-22-22-22-2200200-22−22−2−22−222i−2i2i−2i−2i2i−2i2i0000000000−2i2i2i−2i2-2-222−2−220000i2−i2i2−i2−i2i2−i2i200000000−i2i2i2−i22−2−220000000000000000
χ752-2-22-22-22-2200200-22−22−2−22−22−2i2i−2i2i2i−2i2i−2i00000000002i−2i−2i2i2-2-222−2−220000−i2i2−i2i2i2−i2i2−i200000000i2−i2−i2i22−2−220000000000000000
χ762-2-22-22-22-2200200-22−22−2−22−22−2i2i−2i2i2i−2i2i−2i0000000000−2i2i2i−2i-222-22−2−220000−i2i2−i2i2i2−i2i2−i200000000−i2i2i2−i2−222−20000000000000000
χ772-2-22-22-22-2200200-2−22−222−22−22i−2i2i−2i−2i2i−2i2i00000000002i−2i−2i2i-222-2−222−20000−i2i2−i2i2i2−i2i2−i200000000−i2i2i2−i22−2−220000000000000000
χ782-2-22-22-22-2200200-2−22−222−22−22i−2i2i−2i−2i2i−2i2i0000000000−2i2i2i−2i2-2-22−222−20000−i2i2−i2i2i2−i2i2−i200000000i2−i2−i2i2−222−20000000000000000
χ792-2-22-22-22-2200200-2−22−222−22−2−2i2i−2i2i2i−2i2i−2i00000000002i−2i−2i2i2-2-22−222−20000i2−i2i2−i2−i2i2−i2i200000000−i2i2i2−i2−222−20000000000000000
χ802-2-22-22-22-2200200-2−22−222−22−2−2i2i−2i2i2i−2i2i−2i0000000000−2i2i2i−2i-222-2−222−20000i2−i2i2−i2−i2i2−i2i200000000i2−i2−i2i22−2−220000000000000000
χ8144444444-4-4-4-4-4-4-4-40000000000000000000040000400000000000000000000000000000000000000000000000000000000
χ824444-4-4-4-444-4-4-444-400000000000000000000-40000400000000000000000000000000000000000000000000000000000000
χ8344-4-44i4i−4i−4i00-440−4i4i0000000002i22i2−2i2−2i22222−22−220000000000000000000000−2i22i2−22220000000000000000000000000000000000000000
χ8444-4-44i4i−4i−4i00-440−4i4i000000000−2i2−2i22i22i2−22−22222200000000000000000000002i2−2i222−220000000000000000000000000000000000000000
χ8544-4-4−4i−4i4i4i00-4404i−4i0000000002i22i2−2i2−2i2−22−2222220000000000000000000000−2i22i222−220000000000000000000000000000000000000000
χ8644-4-4−4i−4i4i4i00-4404i−4i000000000−2i2−2i22i22i22222−22−2200000000000000000000002i2−2i2−22220000000000000000000000000000000000000000
χ874-44-44i−4i−4i4i0000000022−22−22222i2−2i2−2i22i222−22−2222−2i22i22i2−2i2000000000000000000000000002-2-22−2i2i2i−2i00000000000000000000000000000000
χ884-44-44i−4i−4i4i0000000022−22−22222i2−2i2−2i22i2−222222−222i2−2i2−2i22i200000000000000000000000000-222-22i−2i−2i2i00000000000000000000000000000000
χ894-44-44i−4i−4i4i00000000−222222−22−2i22i22i2−2i222−22−2222−2i22i22i2−2i200000000000000000000000000-222-22i−2i−2i2i00000000000000000000000000000000
χ904-44-44i−4i−4i4i00000000−222222−22−2i22i22i2−2i2−222222−222i2−2i2−2i22i2000000000000000000000000002-2-22−2i2i2i−2i00000000000000000000000000000000
χ914-44-4−4i4i4i−4i0000000022−22−2222−2i22i22i2−2i222−22−22222i2−2i2−2i22i2000000000000000000000000002-2-222i−2i−2i2i00000000000000000000000000000000
χ924-44-4−4i4i4i−4i0000000022−22−2222−2i22i22i2−2i2−222222−22−2i22i22i2−2i200000000000000000000000000-222-2−2i2i2i−2i00000000000000000000000000000000
χ934-44-4−4i4i4i−4i00000000−222222−222i2−2i2−2i22i222−22−22222i2−2i2−2i22i200000000000000000000000000-222-2−2i2i2i−2i00000000000000000000000000000000
χ944-44-4−4i4i4i−4i00000000−222222−222i2−2i2−2i22i2−222222−22−2i22i22i2−2i2000000000000000000000000002-2-222i−2i−2i2i00000000000000000000000000000000
χ954-4-444-44-4-4400-400422−2222−2222−2222−2200000000000000000000000000−2222−222200000000000000000000000000000000000000000000
χ964-4-444-44-4-4400-4004−2222−2222−2222−22220000000000000000000000000022−2222−2200000000000000000000000000000000000000000000
χ974-4-44-44-444-400-400422−2222−22−2222−222200000000000000000000000000−222222−2200000000000000000000000000000000000000000000
χ984-4-44-44-444-400-4004−2222−222222−2222−220000000000000000000000000022−22−222200000000000000000000000000000000000000000000

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