Finite Group Databasebeta

← Group #229255

Character table — Group #229255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888822444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ121111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ17111-1-11-1-1-1-1-1111-11iiii−i−i−i−i1111-1-1-1-1111-1-1ii−i−iii−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
χ18111-1-11-1-1-1-1-1111-11iiii−i−i−i−i1111-1-1-1-1111-1-1ii−i−i−i−iii−i−iii-1ii−i−i11-1-1iiii−i−i−i−i1-1−ii−iii−iii−i−i-1-111-1-11111-1-1-11-11−ii−ii
χ19111-1-11-1-1-1-1-1111-11iiii−i−i−i−i1111-1-1-1-11-1-111−i−iiiii−i−iii−i−i-1ii−i−i11-1-1iiii−i−i−i−i-11i−ii−i−ii−i−iii11-1-111-1-1-1-111-11-11−ii−ii
χ20111-1-11-1-1-1-1-1111-11iiii−i−i−i−i1111-1-1-1-11-1-111−i−iii−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
χ21111-1-11-1-1-1-1-1111-11iiii−i−i−i−i-1-1-1-11111111-1-1ii−i−iii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiii1-1i−i−iii−i−i−iii11-1-1-1-111-1-1111-1-11i−i−ii
χ22111-1-11-1-1-1-1-1111-11iiii−i−i−i−i-1-1-1-11111111-1-1ii−i−i−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiii1-1−iii−ii−i−i−iii-1-11111-1-1-1-111-111-1−iii−i
χ23111-1-11-1-1-1-1-1111-11iiii−i−i−i−i-1-1-1-111111-1-111−i−iiiii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiii-11i−i−ii−iiii−i−i11-1-1-1-11111-1-1-111-1−iii−i
χ24111-1-11-1-1-1-1-1111-11iiii−i−i−i−i-1-1-1-111111-1-111−i−iii−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiii-11−iii−i−iiii−i−i-1-11111-1-111-1-11-1-11i−i−ii
χ25111-1-11-1-1-1-1-1111-11−i−i−i−iiiii1111-1-1-1-1111-1-1−i−iiiii−i−iii−i−i-1−i−iii11-1-1−i−i−i−iiiii1-1i−ii−i−ii−i−iii-1-111-1-11111-1-1-11-11i−ii−i
χ26111-1-11-1-1-1-1-1111-11−i−i−i−iiiii1111-1-1-1-1111-1-1−i−iii−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
χ27111-1-11-1-1-1-1-1111-11−i−i−i−iiiii1111-1-1-1-11-1-111ii−i−iii−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
χ28111-1-11-1-1-1-1-1111-11−i−i−i−iiiii1111-1-1-1-11-1-111ii−i−i−i−iii−i−iii-1−i−iii11-1-1−i−i−i−iiiii-11−ii−iii−iii−i−i11-1-111-1-1-1-111-11-11i−ii−i
χ29111-1-11-1-1-1-1-1111-11−i−i−i−iiiii-1-1-1-11111111-1-1−i−iiiii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−i1-1i−i−ii−iiii−i−i-1-11111-1-1-1-111-111-1i−i−ii
χ30111-1-11-1-1-1-1-1111-11−i−i−i−iiiii-1-1-1-11111111-1-1−i−iii−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−i1-1−iii−i−iiii−i−i11-1-1-1-111-1-1111-1-11−iii−i
χ31111-1-11-1-1-1-1-1111-11−i−i−i−iiiii-1-1-1-111111-1-111ii−i−iii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−i-11i−i−iii−i−i−iii-1-11111-1-111-1-11-1-11−iii−i
χ32111-1-11-1-1-1-1-1111-11−i−i−i−iiiii-1-1-1-111111-1-111ii−i−i−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−i-11−iii−ii−i−i−iii11-1-1-1-11111-1-1-111-1i−i−ii
χ33222222222-2-22-2-2220000000022222222-20000000022222222-20000-2-2-2-20000000000-2-2-2-200000000000000000000000000
χ34222222222-2-22-2-2220000000022222222-200000000-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000222200000000000000000000000000
χ35222222222-2-22-2-22200000000-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2-2000022220000000000-2-22200000000000000000000000000
χ36222222222-2-22-2-22200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-22222-200002222000000000022-2-200000000000000000000000000
χ3722222222-222-222-2-22222222200000000-22222222200000000-2-2-2-2-2000000000000-2-20000-2-2000000000000000000000000
χ3822222222-222-222-2-22222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000022000022000000000000000000000000
χ3922222222-222-222-2-2-2-2-2-2-2-2-2-200000000-22222-2-2-2-200000000-22222000000000000-2-2000022000000000000000000000000
χ4022222222-222-222-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2222200000000-22222000000000000220000-2-2000000000000000000000000
χ41222-2-22-2-22-2-2-2222-22i2i2i2i−2i−2i−2i−2i00000000-222-2-22i2i−2i−2i000000002−2i−2i2i2i000000000000-220000−2i2i000000000000000000000000
χ42222-2-22-2-22-2-2-2222-22i2i2i2i−2i−2i−2i−2i00000000-2-2-222−2i−2i2i2i000000002−2i−2i2i2i0000000000002-200002i−2i000000000000000000000000
χ43222-2-22-2-22-2-2-2222-2−2i−2i−2i−2i2i2i2i2i00000000-222-2-2−2i−2i2i2i0000000022i2i−2i−2i000000000000-2200002i−2i000000000000000000000000
χ44222-2-22-2-22-2-2-2222-2−2i−2i−2i−2i2i2i2i2i00000000-2-2-2222i2i−2i−2i0000000022i2i−2i−2i0000000000002-20000−2i2i000000000000000000000000
χ45222-2-22-2-2-2222-2-2-22000000002222-2-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i20000-2-2220000000000−2i2i−2i2i00000000000000000000000000
χ46222-2-22-2-2-2222-2-2-22000000002222-2-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i20000-2-22200000000002i−2i2i−2i00000000000000000000000000
χ47222-2-22-2-2-2222-2-2-2200000000-2-2-2-22222-2000000002i2i−2i−2i−2i−2i2i2i2000022-2-20000000000−2i2i2i−2i00000000000000000000000000
χ48222-2-22-2-2-2222-2-2-2200000000-2-2-2-22222-200000000−2i−2i2i2i2i2i−2i−2i2000022-2-200000000002i−2i−2i2i00000000000000000000000000
χ4922-22-2-22-202-202-20022-2-222-2-2i2i2−i2−i2i2i2−i2−i202i−2i2i−2i2i−2i2i−2i0000000000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2000000002−22−2000000002−22−200000000
χ5022-22-2-22-202-202-20022-2-222-2-2i2i2−i2−i2i2i2−i2−i20−2i2i−2i2i−2i2i−2i2i0000000000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200000000−22−2200000000−22−2200000000
χ5122-22-2-22-202-202-20022-2-222-2-2−i2−i2i2i2−i2−i2i2i202i−2i2i−2i2i−2i2i−2i0000000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i200000000−22−2200000000−22−2200000000
χ5222-22-2-22-202-202-20022-2-222-2-2−i2−i2i2i2−i2−i2i2i20−2i2i−2i2i−2i2i−2i2i0000000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2000000002−22−2000000002−22−200000000
χ5322-22-2-22-202-202-200-2-222-2-222i2i2−i2−i2i2i2−i2−i202i−2i2i−2i−2i2i−2i2i0000000000000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i200000000−22−22000000002−22−200000000
χ5422-22-2-22-202-202-200-2-222-2-222i2i2−i2−i2i2i2−i2−i20−2i2i−2i2i2i−2i2i−2i0000000000000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2000000002−22−200000000−22−2200000000
χ5522-22-2-22-202-202-200-2-222-2-222−i2−i2i2i2−i2−i2i2i202i−2i2i−2i−2i2i−2i2i0000000000000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2000000002−22−200000000−22−2200000000
χ5622-22-2-22-202-202-200-2-222-2-222−i2−i2i2i2−i2−i2i2i20−2i2i−2i2i2i−2i2i−2i0000000000000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i200000000−22−22000000002−22−200000000
χ5722-2-22-2-220-2202-2002i2i−2i−2i−2i−2i2i2ii2i2−i2−i2−i2−i2i2i202i−2i−2i2i-222-20000000000000i2−i2−i2i2−2−22222−2−200000000i2−i2−i2i2000000002−2−2200000000
χ5822-2-22-2-220-2202-2002i2i−2i−2i−2i−2i2i2ii2i2−i2−i2−i2−i2i2i20−2i2i2i−2i2-2-220000000000000i2−i2−i2i2−2−22222−2−200000000−i2i2i2−i200000000−222−200000000
χ5922-2-22-2-220-2202-2002i2i−2i−2i−2i−2i2i2i−i2−i2i2i2i2i2−i2−i202i−2i−2i2i-222-20000000000000−i2i2i2−i222−2−2−2−22200000000−i2i2i2−i200000000−222−200000000
χ6022-2-22-2-220-2202-2002i2i−2i−2i−2i−2i2i2i−i2−i2i2i2i2i2−i2−i20−2i2i2i−2i2-2-220000000000000−i2i2i2−i222−2−2−2−22200000000i2−i2−i2i2000000002−2−2200000000
χ6122-2-22-2-220-2202-200−2i−2i2i2i2i2i−2i−2ii2i2−i2−i2−i2−i2i2i202i−2i−2i2i2-2-220000000000000i2−i2−i2i222−2−2−2−22200000000−i2i2i2−i2000000002−2−2200000000
χ6222-2-22-2-220-2202-200−2i−2i2i2i2i2i−2i−2ii2i2−i2−i2−i2−i2i2i20−2i2i2i−2i-222-20000000000000i2−i2−i2i222−2−2−2−22200000000i2−i2−i2i200000000−222−200000000
χ6322-2-22-2-220-2202-200−2i−2i2i2i2i2i−2i−2i−i2−i2i2i2i2i2−i2−i202i−2i−2i2i2-2-220000000000000−i2i2i2−i2−2−22222−2−200000000i2−i2−i2i200000000−222−200000000
χ6422-2-22-2-220-2202-200−2i−2i2i2i2i2i−2i−2i−i2−i2i2i2i2i2−i2−i20−2i2i2i−2i-222-20000000000000−i2i2i2−i2−2−22222−2−200000000−i2i2i2−i2000000002−2−2200000000
χ652-2-2222-2-2200-200-22i2−i2i2−i2i2−i2i2−i22-22-22-22-20000000002i−2i2i−2i2i−2i2i−2i0i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000000000002−22−22−22−2000000000000
χ662-2-2222-2-2200-200-22i2−i2i2−i2i2−i2i2−i22-22-22-22-2000000000−2i2i−2i2i−2i2i−2i2i0i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000000000000−22−22−22−22000000000000
χ672-2-2222-2-2200-200-22i2−i2i2−i2i2−i2i2−i2-22-22-22-220000000002i−2i2i−2i−2i2i−2i2i0i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i20000000000002−22−2−22−22000000000000
χ682-2-2222-2-2200-200-22i2−i2i2−i2i2−i2i2−i2-22-22-22-22000000000−2i2i−2i2i2i−2i2i−2i0i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i2000000000000−22−222−22−2000000000000
χ692-2-2222-2-2200-200-22−i2i2−i2i2−i2i2−i2i22-22-22-22-20000000002i−2i2i−2i2i−2i2i−2i0−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000000000000−22−22−22−22000000000000
χ702-2-2222-2-2200-200-22−i2i2−i2i2−i2i2−i2i22-22-22-22-2000000000−2i2i−2i2i−2i2i−2i2i0−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000000000002−22−22−22−2000000000000
χ712-2-2222-2-2200-200-22−i2i2−i2i2−i2i2−i2i2-22-22-22-220000000002i−2i2i−2i−2i2i−2i2i0−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i2000000000000−22−222−22−2000000000000
χ722-2-2222-2-2200-200-22−i2i2−i2i2−i2i2−i2i2-22-22-22-22000000000−2i2i−2i2i2i−2i2i−2i0−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i20000000000002−22−2−22−22000000000000
χ732-2-2-2-2222-200-200222−22−2−22−222-22-2-22-220000000002-2-222-2-2202−2−2200002−22−2−22−220000000000002−2−222−2−22000000000000
χ742-2-2-2-2222-200-200222−22−2−22−222-22-2-22-22000000000-222-2-222-202−2−2200002−22−2−22−22000000000000−222−2−222−2000000000000
χ752-2-2-2-2222-200-200222−22−2−22−22-22-222-22-20000000002-2-22-222-202−2−220000−22−222−22−20000000000002−2−22−222−2000000000000
χ762-2-2-2-2222-200-200222−22−2−22−22-22-222-22-2000000000-222-22-2-2202−2−220000−22−222−22−2000000000000−222−22−2−22000000000000
χ772-2-2-2-2222-200-20022−22−222−22−22-22-2-22-220000000002-2-222-2-220−222−20000−22−222−22−2000000000000−222−2−222−2000000000000
χ782-2-2-2-2222-200-20022−22−222−22−22-22-2-22-22000000000-222-2-222-20−222−20000−22−222−22−20000000000002−2−222−2−22000000000000
χ792-2-2-2-2222-200-20022−22−222−22−2-22-222-22-20000000002-2-22-222-20−222−200002−22−2−22−22000000000000−222−22−2−22000000000000
χ802-2-2-2-2222-200-20022−22−222−22−2-22-222-22-2000000000-222-22-2-220−222−200002−22−2−22−220000000000002−2−22−222−2000000000000
χ8144444444-4-4-4-4-4-4-4-40000000000000000400000000000000004000000000000000000000000000000000000000000000000
χ82444-4-44-4-4444-4-4-44-4000000000000000040000000000000000-4000000000000000000000000000000000000000000000000
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χ8544-4-44-4-4404-40-4400000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ8644-4-44-4-4404-40-440000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ874-444-4-4-44000000002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ884-444-4-4-44000000002i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ894-444-4-4-4400000000−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ904-444-4-4-4400000000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ914-44-44-44-40000000022−22−2222−222222−222i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ924-44-44-44-40000000022−22−2222−222222−22−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ934-44-44-44-400000000−222222−2222−22−22222i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ944-44-44-44-400000000−222222−2222−22−2222−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ954-4-4444-4-4-4004004-42i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ964-4-4444-4-4-4004004-4−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ974-4-4-4-4444400400-4-422−2222−22−2222−222200000000000000000000000000−222222−2200000000000000000000000000000000000000000000
χ984-4-4-4-4444400400-4-4−2222−222222−2222−220000000000000000000000000022−22−222200000000000000000000000000000000000000000000

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