Finite Group Databasebeta

← Group #110012

Character table — Group #110012

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222224444444444444444444444444444444444448888888888888888444444444444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ511111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1
χ91111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−iiiii−i−i−i−i111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ101111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111
χ111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−i−i−i−i−iiiii111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111
χ121111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1
χ131111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiiiiiii−i−i−i−i111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ141111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1
χ151111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiii−i−i−i−iiiii111111111-1-1-1-1-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ161111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-1-1-1-1-1-1-111111111−i−iii−i−iii1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111
χ171-1-1-111-1-111111-1-1-11111-1-1-1-1111-1-1-11-1-11-111-1-111-1-1ii−i−iii−i−i11111-1-1-1-11111-1-1-1-11-11-1i−ii−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−ii−ii−i
χ181-1-1-111-1-111111-1-1-11111-1-1-1-1111-1-1-11-1-11-111-1-111-1-1ii−i−iii−i−i1-1-1-1-11111-1-1-1-111111-11-1i−ii−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii−ii−ii
χ191-1-1-111-1-111111-1-1-11111-1-1-1-1111-1-1-11-1-11-111-1-111-1-1−i−iii−i−iii11111-1-1-1-11111-1-1-1-11-11-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii−ii−ii
χ201-1-1-111-1-111111-1-1-11111-1-1-1-1111-1-1-11-1-11-111-1-111-1-1−i−iii−i−iii1-1-1-1-11111-1-1-1-111111-11-1−ii−ii−i−iii−i−iii-1-111-1-111ii−i−iii−i−ii−ii−i
χ211-1-1-111-1-111111-1-1-11111-1-1-1-1111-1-1-11-1-11-1-1-111-1-111ii−i−iii−i−i11111-1-1-1-11111-1-1-1-1-11-11i−ii−i−i−iii−i−iii-1-111-1-111ii−i−iii−i−i−ii−ii
χ221-1-1-111-1-111111-1-1-11111-1-1-1-1111-1-1-11-1-11-1-1-111-1-111ii−i−iii−i−i1-1-1-1-11111-1-1-1-11111-11-11i−ii−i−i−iii−i−iii11-1-111-1-1−i−iii−i−iiii−ii−i
χ231-1-1-111-1-111111-1-1-11111-1-1-1-1111-1-1-11-1-11-1-1-111-1-111−i−iii−i−iii11111-1-1-1-11111-1-1-1-1-11-11−ii−iiii−i−iii−i−i-1-111-1-111−i−iii−i−iiii−ii−i
χ241-1-1-111-1-111111-1-1-11111-1-1-1-1111-1-1-11-1-11-1-1-111-1-111−i−iii−i−iii1-1-1-1-11111-1-1-1-11111-11-11−ii−iiii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i−ii−ii
χ251-1-1-1-1-111111-1-111-11111-1-1-1-1-1-1-1111-11-1-11ii−i−i−i−iii11-1-1-1-11111111-1-1-1-1-1-1-1-11111i−i−ii1-1-11−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−iii−i
χ261-1-1-1-1-111111-1-111-11111-1-1-1-1-1-1-1111-11-1-11ii−i−i−i−iii11-1-1-1-1111-1-1-1-111111111-1-1-1-1i−i−ii1-1-11−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1i−i−ii
χ271-1-1-1-1-111111-1-111-11111-1-1-1-1-1-1-1111-11-1-11ii−i−i−i−iii-1-11111-1-111111-1-1-1-1-1-1-1-11111i−i−ii-111-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1i−i−ii
χ281-1-1-1-1-111111-1-111-11111-1-1-1-1-1-1-1111-11-1-11ii−i−i−i−iii-1-11111-1-11-1-1-1-111111111-1-1-1-1i−i−ii-111-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111−iii−i
χ291-1-1-1-1-111111-1-111-11111-1-1-1-1-1-1-1111-11-1-11−i−iiiii−i−i11-1-1-1-11111111-1-1-1-1-1-1-1-11111−iii−i1-1-11ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111i−i−ii
χ301-1-1-1-1-111111-1-111-11111-1-1-1-1-1-1-1111-11-1-11−i−iiiii−i−i11-1-1-1-1111-1-1-1-111111111-1-1-1-1−iii−i1-1-11ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1−iii−i
χ311-1-1-1-1-111111-1-111-11111-1-1-1-1-1-1-1111-11-1-11−i−iiiii−i−i-1-11111-1-111111-1-1-1-1-1-1-1-11111−iii−i-111-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−iii−i
χ321-1-1-1-1-111111-1-111-11111-1-1-1-1-1-1-1111-11-1-11−i−iiiii−i−i-1-11111-1-11-1-1-1-111111111-1-1-1-1−iii−i-111-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111i−i−ii
χ33222222222222222222-2-222-2-222-22-2-2-22-2-2-22222222200000000-20000000000000000-2-2-2-200000000000000000000000000000000
χ34222222222222222222-2-222-2-222-22-2-2-22-2-2-2-2-2-2-2-2-2-2-200000000-20000000000000000222200000000000000000000000000000000
χ352222222222222222-2-222-2-222-2-22-2222-2-2-2-20000000022222222-200000000000000000000-2-2-2-20000000000000000000000000000
χ362222222222222222-2-222-2-222-2-22-2222-2-2-2-200000000-2-2-2-2-2-2-2-2-20000000000000000000022220000000000000000000000000000
χ372222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222000000000000000020000000000000000000000002-22-22-22-200000000000000000000
χ382222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222200000000000000002000000000000000000000000-22-22-22-2200000000000000000000
χ392222-2-2-2-2222-2-2-2-2222-2-222-2-2-2-22-2222-2-2222i2i2i2i−2i−2i−2i−2i00000000-20000000000000000−2i−2i2i2i00000000000000000000000000000000
χ402222-2-2-2-2222-2-2-2-2222-2-222-2-2-2-22-2222-2-222−2i−2i−2i−2i2i2i2i2i00000000-200000000000000002i2i−2i−2i00000000000000000000000000000000
χ412222-2-2-2-2222-2-2-2-22-2-222-2-22222-22-2-2-22-222000000002i2i2i2i−2i−2i−2i−2i-200000000000000000000−2i−2i2i2i0000000000000000000000000000
χ422222-2-2-2-2222-2-2-2-22-2-222-2-22222-22-2-2-22-22200000000−2i−2i−2i−2i2i2i2i2i-2000000000000000000002i2i−2i−2i0000000000000000000000000000
χ432222-2-2-2-2222-2-2-2-22-2-2-2-2-2-2-2-2222222222-2-2000000000000000020000000000000000000000002-22-2-22-2200000000000000000000
χ442222-2-2-2-2222-2-2-2-22-2-2-2-2-2-2-2-2222222222-2-200000000000000002000000000000000000000000-22-222-22-200000000000000000000
χ45222-2222-22-2-2-2-22-2-2002-2002-200202-2-20000000000002-22-22-22-2022−2−222−2−222−2−222−2−20000000000000000000000002−22−22−22−20000
χ46222-2222-22-2-2-2-22-2-2002-2002-200202-2-20000000000002-22-22-22-20−2−222−2−222−2−222−2−222000000000000000000000000−22−22−22−220000
χ47222-2222-22-2-2-2-22-2-2002-2002-200202-2-2000000000000-22-22-22-22022−2−222−2−222−2−222−2−2000000000000000000000000−22−22−22−220000
χ48222-2222-22-2-2-2-22-2-2002-2002-200202-2-2000000000000-22-22-22-220−2−222−2−222−2−222−2−2220000000000000000000000002−22−22−22−20000
χ49222-2-2-2-222-2-222-22-2002-2002-200-20-2220000000000002i−2i2i−2i−2i2i−2i2i022−2−222−2−2−2−222−2−222000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ50222-2-2-2-222-2-222-22-2002-2002-200-20-2220000000000002i−2i2i−2i−2i2i−2i2i0−2−222−2−22222−2−222−2−2000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ51222-2-2-2-222-2-222-22-2002-2002-200-20-222000000000000−2i2i−2i2i2i−2i2i−2i022−2−222−2−2−2−222−2−222000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ52222-2-2-2-222-2-222-22-2002-2002-200-20-222000000000000−2i2i−2i2i2i−2i2i−2i0−2−222−2−22222−2−222−2−2000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ5322-222-222-22-22-2-2-2-22-2002-2002-202000-20002-22-22-22-20000000002−22−22−22−22−22−22−22−200000000000000002−22−22−22−2000000000000
χ5422-222-222-22-22-2-2-2-22-2002-2002-202000-20002-22-22-22-2000000000−22−22−22−22−22−22−22−220000000000000000−22−22−22−22000000000000
χ5522-222-222-22-22-2-2-2-22-2002-2002-202000-2000-22-22-22-220000000002−22−22−22−22−22−22−22−20000000000000000−22−22−22−22000000000000
χ5622-222-222-22-22-2-2-2-22-2002-2002-202000-2000-22-22-22-22000000000−22−22−22−22−22−22−22−2200000000000000002−22−22−22−2000000000000
χ5722-22-22-2-2-22-2-2222-22-2002-200-220-200020002i−2i2i−2i−2i2i−2i2i0000000002−22−22−22−2−22−22−22−220000000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ5822-22-22-2-2-22-2-2222-22-2002-200-220-200020002i−2i2i−2i−2i2i−2i2i000000000−22−22−22−222−22−22−22−20000000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ5922-22-22-2-2-22-2-2222-22-2002-200-220-20002000−2i2i−2i2i2i−2i2i−2i0000000002−22−22−22−2−22−22−22−220000000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ6022-22-22-2-2-22-2-2222-22-2002-200-220-20002000−2i2i−2i2i2i−2i2i−2i000000000−22−22−22−222−22−22−22−20000000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ612-22-22-2-2-2-22-22-22222-200-22002-20-200020002-2-222-2-220000000002−22−2−22−222−22−2−22−2200000000000000002−2−222−2−22000000000000
χ622-22-22-2-2-2-22-22-22222-200-22002-20-200020002-2-222-2-22000000000−22−222−22−2−22−222−22−20000000000000000−222−2−222−2000000000000
χ632-22-22-2-2-2-22-22-22222-200-22002-20-20002000-222-2-222-20000000002−22−2−22−222−22−2−22−220000000000000000−222−2−222−2000000000000
χ642-22-22-2-2-2-22-22-22222-200-22002-20-20002000-222-2-222-2000000000−22−222−22−2−22−222−22−200000000000000002−2−222−2−22000000000000
χ652-22-2-2222-22-2-22-2-222-200-2200-2202000-20002i−2i−2i2i−2i2i2i−2i0000000002−22−2−22−22−22−222−22−20000000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ662-22-2-2222-22-2-22-2-222-200-2200-2202000-20002i−2i−2i2i−2i2i2i−2i000000000−22−222−22−22−22−2−22−220000000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ672-22-2-2222-22-2-22-2-222-200-2200-2202000-2000−2i2i2i−2i2i−2i−2i2i0000000002−22−2−22−22−22−222−22−20000000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ682-22-2-2222-22-2-22-2-222-200-2200-2202000-2000−2i2i2i−2i2i−2i−2i2i000000000−22−222−22−22−22−2−22−220000000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ692-2-2222-222-2-2-2-2-222002-200-220020-22-20000000000002i−2i−2i2i2i−2i−2i2i022−2−2−2−22222−2−2−2−222000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ702-2-2222-222-2-2-2-2-222002-200-220020-22-20000000000002i−2i−2i2i2i−2i−2i2i0−2−22222−2−2−2−22222−2−2000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ712-2-2222-222-2-2-2-2-222002-200-220020-22-2000000000000−2i2i2i−2i−2i2i2i−2i022−2−2−2−22222−2−2−2−222000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ722-2-2222-222-2-2-2-2-222002-200-220020-22-2000000000000−2i2i2i−2i−2i2i2i−2i0−2−22222−2−2−2−22222−2−2000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ732-2-22-2-22-22-2-2222-22002-200-2200-202-220000000000002-2-22-222-2022−2−2−2−222−2−22222−2−20000000000000000000000002−2−22−222−20000
χ742-2-22-2-22-22-2-2222-22002-200-2200-202-220000000000002-2-22-222-20−2−22222−2−222−2−2−2−222000000000000000000000000−222−22−2−220000
χ752-2-22-2-22-22-2-2222-22002-200-2200-202-22000000000000-222-22-2-22022−2−2−2−222−2−22222−2−2000000000000000000000000−222−22−2−220000
χ762-2-22-2-22-22-2-2222-22002-200-2200-202-22000000000000-222-22-2-220−2−22222−2−222−2−2−2−2220000000000000000000000002−2−22−222−20000
χ772-2-2-222-2-222222-2-2-222-2-2-2-22222-2-222-2-22-2222-2-222-2-200000000-20000000000000000-22-2200000000000000000000000000000000
χ782-2-2-222-2-222222-2-2-222-2-2-2-22222-2-222-2-22-22-2-222-2-22200000000-200000000000000002-22-200000000000000000000000000000000
χ792-2-2-222-2-222222-2-2-2-2-22222-2-2-2-222-2-2222-22000000002i2i−2i−2i2i2i−2i−2i-200000000000000000000−2i2i−2i2i0000000000000000000000000000
χ802-2-2-222-2-222222-2-2-2-2-22222-2-2-2-222-2-2222-2200000000−2i−2i2i2i−2i−2i2i2i-2000000000000000000002i−2i2i−2i0000000000000000000000000000
χ812-2-2-222-2-222222-2-2-2-2-2-2-22222-2-2-2222-22-22-2000000000000000020000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ822-2-2-222-2-222222-2-2-2-2-2-2-22222-2-2-2222-22-22-200000000000000002000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ832-2-2-2-2-222222-2-222-222-2-2-2-222-2-222-2-22222-22i2i−2i−2i−2i−2i2i2i00000000-20000000000000000−2i2i2i−2i00000000000000000000000000000000
χ842-2-2-2-2-222222-2-222-222-2-2-2-222-2-222-2-22222-2−2i−2i2i2i2i2i−2i−2i00000000-200000000000000002i−2i−2i2i00000000000000000000000000000000
χ852-2-2-2-2-222222-2-222-2-2-22222-2-222-2-222-2-222-20000000022-2-2-2-222-200000000000000000000-222-20000000000000000000000000000
χ862-2-2-2-2-222222-2-222-2-2-22222-2-222-2-222-2-222-200000000-2-22222-2-2-2000000000000000000002-2-220000000000000000000000000000
χ872-2-2-2-2-222222-2-222-2-2-2-2-22222222-2-2-22-2-2-22000000000000000020000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ882-2-2-2-2-222222-2-222-2-2-2-2-22222222-2-2-22-2-2-2200000000000000002000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
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χ9344-4-44-44-4-4-44-44-4440000000000000000000000000000000000002-2-222-2-222-2-222-2-22000000000000000000000000000000000000
χ9444-4-44-44-4-4-44-44-444000000000000000000000000000000000000-222-2-222-2-222-2-222-2000000000000000000000000000000000000
χ9544-4-4-44-44-4-444-44-440000000000000000000000000000000000002-2-222-2-22-222-2-222-2000000000000000000000000000000000000
χ9644-4-4-44-44-4-444-44-44000000000000000000000000000000000000-222-2-222-22-2-222-2-22000000000000000000000000000000000000
χ974-4444-4-44-4-44-444-4-40000000000000000000000000000000000002-2-22-222-22-2-22-222-2000000000000000000000000000000000000
χ984-4444-4-44-4-44-444-4-4000000000000000000000000000000000000-222-22-2-22-222-22-2-22000000000000000000000000000000000000
χ994-444-444-4-4-444-4-44-40000000000000000000000000000000000002-2-22-222-2-222-22-2-22000000000000000000000000000000000000
χ1004-444-444-4-4-444-4-44-4000000000000000000000000000000000000-222-22-2-222-2-22-222-2000000000000000000000000000000000000
χ1014-44-44-4-4-4-44-44-4444-44004-400-4404000-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-4-4444-44-4-44-4-44-44004-4004-40-40004000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4444-444-4-4-4-4-44400-44004-400-404-440000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-4-44-44-4-4444-4400-44004-40040-44-40000000000000000000000000000000000000000000000000000000000000000000000000

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