Finite Group Databasebeta

← Group #229261

Character table — Group #229261

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888822444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ101111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1711-1-111-1-1-11-1-1-1111iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i1ii−i−iii−i−i-1ii−i−i11-1-1iiii−i−i−i−i1-1i−ii−ii−iii−i−i11-1-111-1-111-1-11-11-1i−ii−i
χ1811-1-111-1-1-11-1-1-1111iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i1−i−iii−i−iii-1ii−i−i11-1-1iiii−i−i−i−i1-1i−i−ii−iiii−i−i-1-111-1-11111-1-1-11-11−ii−ii
χ1911-1-111-1-1-11-1-1-1111iiii−i−i−i−i1111-1-1-1-1-1-111−i−iii1ii−i−iii−i−i-1ii−i−i11-1-1iiii−i−i−i−i-11−iii−ii−i−i−iii11-1-111-1-1-1-111-11-11−ii−ii
χ2011-1-111-1-1-11-1-1-1111iiii−i−i−i−i1111-1-1-1-1-1-111−i−iii1−i−iii−i−iii-1ii−i−i11-1-1iiii−i−i−i−i-11−ii−ii−ii−i−iii-1-111-1-111-1-1111-11-1i−ii−i
χ2111-1-111-1-1-11-1-1-1111iiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i1ii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiii1-1i−ii−i−ii−i−iii11-1-1-1-111-1-1111-1-11i−i−ii
χ2211-1-111-1-1-11-1-1-1111iiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i1−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiii1-1i−i−iii−i−i−iii-1-11111-1-1-1-111-111-1−iii−i
χ2311-1-111-1-1-11-1-1-1111iiii−i−i−i−i-1-1-1-11111-1-111−i−iii1ii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiii-11−iii−i−iiii−i−i11-1-1-1-11111-1-1-111-1−iii−i
χ2411-1-111-1-1-11-1-1-1111iiii−i−i−i−i-1-1-1-11111-1-111−i−iii1−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiii-11−ii−iii−iii−i−i-1-11111-1-111-1-11-1-11i−i−ii
χ2511-1-111-1-1-11-1-1-1111−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii1ii−i−iii−i−i-1−i−iii11-1-1−i−i−i−iiiii1-1−iii−ii−i−i−iii-1-111-1-11111-1-1-11-11i−ii−i
χ2611-1-111-1-1-11-1-1-1111−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii1−i−iii−i−iii-1−i−iii11-1-1−i−i−i−iiiii1-1−ii−ii−ii−i−iii11-1-111-1-111-1-11-11-1−ii−ii
χ2711-1-111-1-1-11-1-1-1111−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i1ii−i−iii−i−i-1−i−iii11-1-1−i−i−i−iiiii-11i−ii−ii−iii−i−i-1-111-1-111-1-1111-11-1−ii−ii
χ2811-1-111-1-1-11-1-1-1111−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i1−i−iii−i−iii-1−i−iii11-1-1−i−i−i−iiiii-11i−i−ii−iiii−i−i11-1-111-1-1-1-111-11-11i−ii−i
χ2911-1-111-1-1-11-1-1-1111−i−i−i−iiiii-1-1-1-1111111-1-1−i−iii1ii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−i1-1−iii−i−iiii−i−i-1-11111-1-1-1-111-111-1i−i−ii
χ3011-1-111-1-1-11-1-1-1111−i−i−i−iiiii-1-1-1-1111111-1-1−i−iii1−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−i1-1−ii−iii−iii−i−i11-1-1-1-111-1-1111-1-11−iii−i
χ3111-1-111-1-1-11-1-1-1111−i−i−i−iiiii-1-1-1-11111-1-111ii−i−i1ii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−i-11i−ii−i−ii−i−iii-1-11111-1-111-1-11-1-11−iii−i
χ3211-1-111-1-1-11-1-1-1111−i−i−i−iiiii-1-1-1-11111-1-111ii−i−i1−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−i-11i−i−iii−i−i−iii11-1-1-1-11111-1-1-111-1i−i−ii
χ332222222222-2-22-2-22000000002222222200000000-222222222-20000-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ342222222222-2-22-2-22000000002222222200000000-2-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000002222000000000000000000000000
χ352222222222-2-22-2-2200000000-2-2-2-2-2-2-2-200000000-22222-2-2-2-2-200002222000000000000-2-222000000000000000000000000
χ362222222222-2-22-2-2200000000-2-2-2-2-2-2-2-200000000-2-2-2-2-22222-20000222200000000000022-2-2000000000000000000000000
χ3722222222-2-222-222-2222222220000000022222222-200000000-2-2-2-2-2000000000000-2-2-2-20000000000000000000000000000
χ3822222222-2-222-222-22222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000022220000000000000000000000000000
χ3922222222-2-222-222-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2-200000000-22222000000000000-2-2220000000000000000000000000000
χ4022222222-2-222-222-2-2-2-2-2-2-2-2-200000000-2-2-2-22222-200000000-2222200000000000022-2-20000000000000000000000000000
χ412222-2-2-2-2-2-200200222−2−222−2−222-2-222-2-20000000002i−2i2i−2i2i−2i2i−2i02−22−2000022−2−222−2−2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ422222-2-2-2-2-2-200200222−2−222−2−222-2-222-2-2000000000−2i2i−2i2i−2i2i−2i2i02−22−2000022−2−222−2−2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ432222-2-2-2-2-2-200200222−2−222−2−2-2-222-2-2220000000002i−2i2i−2i−2i2i−2i2i02−22−20000−2−222−2−222000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ442222-2-2-2-2-2-200200222−2−222−2−2-2-222-2-222000000000−2i2i−2i2i2i−2i2i−2i02−22−20000−2−222−2−222000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ452222-2-2-2-2-2-2002002−2−222−2−22222-2-222-2-20000000002i−2i2i−2i2i−2i2i−2i0−22−220000−2−222−2−222000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ462222-2-2-2-2-2-2002002−2−222−2−22222-2-222-2-2000000000−2i2i−2i2i−2i2i−2i2i0−22−220000−2−222−2−222000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ472222-2-2-2-2-2-2002002−2−222−2−222-2-222-2-2220000000002i−2i2i−2i−2i2i−2i2i0−22−22000022−2−222−2−2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ482222-2-2-2-2-2-2002002−2−222−2−222-2-222-2-222000000000−2i2i−2i2i2i−2i2i−2i0−22−22000022−2−222−2−2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ4922-2-222-2-22-2-2-2222-22i2i2i2i−2i−2i−2i−2i0000000022-2-22i2i−2i−2i-2000000002−2i−2i2i2i000000000000-22−2i2i0000000000000000000000000000
χ5022-2-222-2-22-2-2-2222-22i2i2i2i−2i−2i−2i−2i00000000-2-222−2i−2i2i2i-2000000002−2i−2i2i2i0000000000002-22i−2i0000000000000000000000000000
χ5122-2-222-2-22-2-2-2222-2−2i−2i−2i−2i2i2i2i2i0000000022-2-2−2i−2i2i2i-20000000022i2i−2i−2i000000000000-222i−2i0000000000000000000000000000
χ5222-2-222-2-22-2-2-2222-2−2i−2i−2i−2i2i2i2i2i00000000-2-2222i2i−2i−2i-20000000022i2i−2i−2i0000000000002-2−2i2i0000000000000000000000000000
χ5322-2-222-2-2-2222-2-2-22000000002222-2-2-2-200000000-22i2i−2i−2i2i2i−2i−2i20000-2-222000000000000−2i2i−2i2i000000000000000000000000
χ5422-2-222-2-2-2222-2-2-22000000002222-2-2-2-200000000-2−2i−2i2i2i−2i−2i2i2i20000-2-2220000000000002i−2i2i−2i000000000000000000000000
χ5522-2-222-2-2-2222-2-2-2200000000-2-2-2-2222200000000-22i2i−2i−2i−2i−2i2i2i2000022-2-2000000000000−2i2i2i−2i000000000000000000000000
χ5622-2-222-2-2-2222-2-2-2200000000-2-2-2-2222200000000-2−2i−2i2i2i2i2i−2i−2i2000022-2-20000000000002i−2i−2i2i000000000000000000000000
χ5722-2-2-2-2222-200-2002i2i2−i2−i2−i2−i2i2i222-2-2-2-2220000000002-2-222-2-220i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ5822-2-2-2-2222-200-2002i2i2−i2−i2−i2−i2i2i222-2-2-2-222000000000-222-2-222-20i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ5922-2-2-2-2222-200-2002i2i2−i2−i2−i2−i2i2i2-2-22222-2-20000000002-2-22-222-20i2−i2−i2i20000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ6022-2-2-2-2222-200-2002i2i2−i2−i2−i2−i2i2i2-2-22222-2-2000000000-222-22-2-220i2−i2−i2i20000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ6122-2-2-2-2222-200-2002−i2−i2i2i2i2i2−i2−i222-2-2-2-2220000000002-2-222-2-220−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ6222-2-2-2-2222-200-2002−i2−i2i2i2i2i2−i2−i222-2-2-2-222000000000-222-2-222-20−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ6322-2-2-2-2222-200-2002−i2−i2i2i2i2i2−i2−i2-2-22222-2-20000000002-2-22-222-20−i2i2i2−i20000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ6422-2-2-2-2222-200-2002−i2−i2i2i2i2i2−i2−i2-2-22222-2-2000000000-222-22-2-220−i2i2i2−i20000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ652-22-22-22-2002-202-202-22-22-22-2i2−i2i2−i2i2−i2i2−i22i−2i2i−2i2i−2i2i−2i00000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000002−22−2000000002−22−200000000
χ662-22-22-22-2002-202-202-22-22-22-2i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i−2i2i−2i2i00000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000−22−2200000000−22−2200000000
χ672-22-22-22-2002-202-202-22-22-22-2−i2i2−i2i2−i2i2−i2i22i−2i2i−2i2i−2i2i−2i00000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000−22−2200000000−22−2200000000
χ682-22-22-22-2002-202-202-22-22-22-2−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i−2i2i−2i2i00000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000002−22−2000000002−22−200000000
χ692-22-22-22-2002-202-20-22-22-22-22i2−i2i2−i2i2−i2i2−i22i−2i2i−2i−2i2i−2i2i00000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000−22−22000000002−22−200000000
χ702-22-22-22-2002-202-20-22-22-22-22i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i2i−2i2i−2i00000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000002−22−200000000−22−2200000000
χ712-22-22-22-2002-202-20-22-22-22-22−i2i2−i2i2−i2i2−i2i22i−2i2i−2i−2i2i−2i2i00000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000002−22−200000000−22−2200000000
χ722-22-22-22-2002-202-20-22-22-22-22−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i2i−2i2i−2i00000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000−22−22000000002−22−200000000
χ732-2-222-2-2200-2202-202i−2i2i−2i−2i2i−2i2ii2−i2i2−i2−i2i2−i2i22i−2i−2i2i-222-200000000000000i2−i2−i2i2−22−222−22−200000000i2−i2−i2i2000000002−2−2200000000
χ742-2-222-2-2200-2202-202i−2i2i−2i−2i2i−2i2ii2−i2i2−i2−i2i2−i2i2−2i2i2i−2i2-2-2200000000000000i2−i2−i2i2−22−222−22−200000000−i2i2i2−i200000000−222−200000000
χ752-2-222-2-2200-2202-202i−2i2i−2i−2i2i−2i2i−i2i2−i2i2i2−i2i2−i22i−2i−2i2i-222-200000000000000−i2i2i2−i22−22−2−22−2200000000−i2i2i2−i200000000−222−200000000
χ762-2-222-2-2200-2202-202i−2i2i−2i−2i2i−2i2i−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i2-2-2200000000000000−i2i2i2−i22−22−2−22−2200000000i2−i2−i2i2000000002−2−2200000000
χ772-2-222-2-2200-2202-20−2i2i−2i2i2i−2i2i−2ii2−i2i2−i2−i2i2−i2i22i−2i−2i2i2-2-2200000000000000i2−i2−i2i22−22−2−22−2200000000−i2i2i2−i2000000002−2−2200000000
χ782-2-222-2-2200-2202-20−2i2i−2i2i2i−2i2i−2ii2−i2i2−i2−i2i2−i2i2−2i2i2i−2i-222-200000000000000i2−i2−i2i22−22−2−22−2200000000i2−i2−i2i200000000−222−200000000
χ792-2-222-2-2200-2202-20−2i2i−2i2i2i−2i2i−2i−i2i2−i2i2i2−i2i2−i22i−2i−2i2i2-2-2200000000000000−i2i2i2−i2−22−222−22−200000000i2−i2−i2i200000000−222−200000000
χ802-2-222-2-2200-2202-20−2i2i−2i2i2i−2i2i−2i−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i-222-200000000000000−i2i2i2−i2−22−222−22−200000000−i2i2i2−i2000000002−2−2200000000
χ8144444444-4-4-4-4-4-4-4-40000000000000000000000004000000004000000000000000000000000000000000000000000000000
χ824444-4-4-4-44400-400-42222−22−222222−22−2200000000000000000000000000−2222−222200000000000000000000000000000000000000000000
χ834444-4-4-4-44400-400-4−22−222222−22−2222220000000000000000000000000022−2222−2200000000000000000000000000000000000000000000
χ8444-4-444-4-44-4444-4-4-4000000000000000000000000400000000-4000000000000000000000000000000000000000000000000
χ8544-4-4-4-444-4400400-42i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ8644-4-4-4-444-4400400-4−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ874-44-44-44-400-440-440000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ884-44-44-44-400-440-44000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ894-44-4-44-440000000022−22−222222−22−22222i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ904-44-4-44-440000000022−22−222222−22−2222−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ914-44-4-44-4400000000−222222−22−222222−222i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ924-44-4-44-4400000000−222222−22−222222−22−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ934-4-444-4-44004-40-440000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ944-4-444-4-44004-40-44000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ954-4-44-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ964-4-44-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ974-4-44-444-400000000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ984-4-44-444-400000000−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000-222-22-2-2200000000000000000000000000000000

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