Finite Group Databasebeta

← Group #376155

Character table — Group #376155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222224444444444444444222244444444444444448888888888888888222244444444444444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ711111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ1711111-1-1-1-1-111-1-11-1iiii−i−i−i−i11-1-111-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−i1-111-1-1i−iii−i−iii−i−i11-1-11-1i−i
χ1811111-1-1-1-1-111-1-11-1iiii−i−i−i−i11-1-111-1-111-1-1ii−i−iii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-11111-1-1−i−iii1-111-1-1i−iii−i−i−i−iii-1-111-11−ii
χ1911111-1-1-1-1-111-1-11-1iiii−i−i−i−i11-1-111-1-111-1-1ii−i−iii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iii1-1-1-111i−i−i−iiiii−i−i11-1-1-11−ii
χ2011111-1-1-1-1-111-1-11-1iiii−i−i−i−i11-1-111-1-111-1-1ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1-1-111ii−i−i1-1-1-111i−i−i−iii−i−iii-1-1111-1i−i
χ2111111-1-1-1-1-111-1-11-1iiii−i−i−i−i11-1-111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−i-11-1-111−ii−i−iii−i−iii-1-111-11−ii
χ2211111-1-1-1-1-111-1-11-1iiii−i−i−i−i11-1-111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-11111-1-1−i−iii-11-1-111−ii−i−iiiii−i−i11-1-11-1i−i
χ2311111-1-1-1-1-111-1-11-1iiii−i−i−i−i11-1-111-1-1-1-111ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iii-1111-1-1−iiii−i−i−i−iii-1-1111-1i−i
χ2411111-1-1-1-1-111-1-11-1iiii−i−i−i−i11-1-111-1-1-1-111ii−i−i−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1-1-111ii−i−i-1111-1-1−iiii−i−iii−i−i11-1-1-11−ii
χ2511111-1-1-1-1-111-1-11-1−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1-1-111−i−iii1-1-1-111−iiii−i−iii−i−i-1-1111-1−ii
χ2611111-1-1-1-1-111-1-11-1−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111-1-111ii−i−i1-1-1-111−iiii−i−i−i−iii11-1-1-11i−i
χ2711111-1-1-1-1-111-1-11-1−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-11111-1-1ii−i−i1-111-1-1−ii−i−iiiii−i−i-1-111-11i−i
χ2811111-1-1-1-1-111-1-11-1−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−iii1-111-1-1−ii−i−iii−i−iii11-1-11-1−ii
χ2911111-1-1-1-1-111-1-11-1−i−i−i−iiiii11-1-111-1-1-1-111−i−iiiii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1-1-111−i−iii-1111-1-1i−i−i−iii−i−iii11-1-1-11i−i
χ3011111-1-1-1-1-111-1-11-1−i−i−i−iiiii11-1-111-1-1-1-111−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111-1-111ii−i−i-1111-1-1i−i−i−iiiii−i−i-1-1111-1−ii
χ3111111-1-1-1-1-111-1-11-1−i−i−i−iiiii11-1-111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-11111-1-1ii−i−i-11-1-111i−iii−i−i−i−iii11-1-11-1−ii
χ3211111-1-1-1-1-111-1-11-1−i−i−i−iiiii11-1-111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−iii-11-1-111i−iii−i−iii−i−i-1-111-11i−i
χ33222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000-2-20000-2-20000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000220000220000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000-2-20000220000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000220000-2-20000000000000000
χ3722222-2-2-2-2-222-2-22-22i2i2i2i−2i−2i−2i−2i-2-222-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000-220000−2i2i0000000000000000
χ3822222-2-2-2-2-222-2-22-22i2i2i2i−2i−2i−2i−2i-2-222-2-222-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000002-200002i−2i0000000000000000
χ3922222-2-2-2-2-222-2-22-2−2i−2i−2i−2i2i2i2i2i-2-222-2-22222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000-2200002i−2i0000000000000000
χ4022222-2-2-2-2-222-2-22-2−2i−2i−2i−2i2i2i2i2i-2-222-2-222-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000002-20000−2i2i0000000000000000
χ41222-2-222-22-22-2-2-2-222i2i−2i−2i2i2i−2i−2i000000002-22-200002i−2i2i−2i0000000022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000000000002−22−2i2−i2i2−i20000
χ42222-2-222-22-22-2-2-2-222i2i−2i−2i2i2i−2i−2i000000002-22-200002i−2i2i−2i00000000−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000000000000000−22−22−i2i2−i2i20000
χ43222-2-222-22-22-2-2-2-222i2i−2i−2i2i2i−2i−2i00000000-22-220000−2i2i−2i2i0000000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000000000000000−22−22−i2i2−i2i20000
χ44222-2-222-22-22-2-2-2-222i2i−2i−2i2i2i−2i−2i00000000-22-220000−2i2i−2i2i00000000−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000000000002−22−2i2−i2i2−i20000
χ45222-2-222-22-22-2-2-2-22−2i−2i2i2i−2i−2i2i2i000000002-22-20000−2i2i−2i2i0000000022−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000000000002−22−2−i2i2−i2i20000
χ46222-2-222-22-22-2-2-2-22−2i−2i2i2i−2i−2i2i2i000000002-22-20000−2i2i−2i2i00000000−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000000000000000−22−22i2−i2i2−i20000
χ47222-2-222-22-22-2-2-2-22−2i−2i2i2i−2i−2i2i2i00000000-22-2200002i−2i2i−2i0000000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000000000000000−22−22i2−i2i2−i20000
χ48222-2-222-22-22-2-2-2-22−2i−2i2i2i−2i−2i2i2i00000000-22-2200002i−2i2i−2i00000000−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000000000002−22−2−i2i2−i2i20000
χ49222-2-2-2-22-222-222-2-222-2-2-2-222000000002-2-2200002-2-2200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ50222-2-2-2-22-222-222-2-222-2-2-2-222000000002-2-2200002-2-2200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ51222-2-2-2-22-222-222-2-222-2-2-2-22200000000-222-20000-222-200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ52222-2-2-2-22-222-222-2-222-2-2-2-22200000000-222-20000-222-200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ53222-2-2-2-22-222-222-2-2-2-22222-2-2000000002-2-220000-222-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ54222-2-2-2-22-222-222-2-2-2-22222-2-2000000002-2-220000-222-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ55222-2-2-2-22-222-222-2-2-2-22222-2-200000000-222-200002-2-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ56222-2-2-2-22-222-222-2-2-2-22222-2-200000000-222-200002-2-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
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χ702-22-2-2222-2-2-222-22-2−2i2i−2i2i−2i2i−2i2i2-22-22-2-220000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i000000000000000000002-22-20000000000000000000000000000
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χ722-22-2-2222-2-2-222-22-2−2i2i−2i2i−2i2i−2i2i-22-22-222-200002i−2i2i−2i000000000000000000000000000000000000000000-22-22002i−2i2i−2i000000000000
χ732-22-2-2-2-2-222-22-22222-22-2-22-222-2-222-22-200002-2-2200002-22-2-22-22000000000000000000002-2-220000000000000000000000000000
χ742-22-2-2-2-2-222-22-22222-22-2-22-222-2-222-22-200002-2-220000-22-222-22-200000000000000000000-222-20000000000000000000000000000
χ752-22-2-2-2-2-222-22-22222-22-2-22-22-222-2-22-220000-222-20000000000000000000000000000000000000000002-2-22002-2-22000000000000
χ762-22-2-2-2-2-222-22-22222-22-2-22-22-222-2-22-220000-222-2000000000000000000000000000000000000000000-222-200-222-2000000000000
χ772-22-2-2-2-2-222-22-2222-22-222-22-22-2-222-22-20000-222-200002-22-2-22-2200000000000000000000-222-20000000000000000000000000000
χ782-22-2-2-2-2-222-22-2222-22-222-22-22-2-222-22-20000-222-20000-22-222-22-2000000000000000000002-2-220000000000000000000000000000
χ792-22-2-2-2-2-222-22-2222-22-222-22-2-222-2-22-2200002-2-220000000000000000000000000000000000000000002-2-2200-222-2000000000000
χ802-22-2-2-2-2-222-22-2222-22-222-22-2-222-2-22-2200002-2-22000000000000000000000000000000000000000000-222-2002-2-22000000000000
χ812-2-2-222-222-22-2-222-2000000002-222-22-2-20000000000002i−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i−2i2i−2i000000002-22-200000000000000000000000000000000
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χ852-2-2-22-22-2-222-22-222000000002-2-2-2-22220000000000002-2-22-222-22-22-2-22-22000000002-2-2200000000000000000000000000000000
χ862-2-2-22-22-2-222-22-222000000002-2-2-2-22220000000000002-2-22-222-2-22-222-22-200000000-222-200000000000000000000000000000000
χ872-2-2-22-22-2-222-22-222000000002-2-2-2-2222000000000000-222-22-2-222-22-2-22-2200000000-222-200000000000000000000000000000000
χ882-2-2-22-22-2-222-22-222000000002-2-2-2-2222000000000000-222-22-2-22-22-222-22-2000000002-2-2200000000000000000000000000000000
χ8944-44-44-44-44-4-4-4-44400000000-4-4-4444-44000000000000000000000000000000000000000000000000000000000000000000000000
χ9044-44-4-44-44-4-4-4444-400000000-4-44-4444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-444-4-4-4-4-4444-440000000000000000000000000000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ9244-4-444-4-4-4-4-4444-4400000000000000000000000000000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ9344-4-44-44444-44-4-4-4-40000000000000000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ9444-4-44-44444-44-4-4-4-400000000000000000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000
χ954-444444-4-44-4-4-44-4-44-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ964-444444-4-44-4-4-44-4-4-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ974-4444-4-444-4-4-44-4-444i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ984-4444-4-444-4-4-44-4-44−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ994-4-44-44-4-444444-4-4-40000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ1004-4-44-44-4-444444-4-4-4000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ1014-4-44-4-444-4-444-44-4400000000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ1024-4-44-4-444-4-444-44-44000000000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ1034-4-4-444-444-44-4-444-400000000-44-4-44-444000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-44-44-4-444-44-44400000000-44444-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000

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