Finite Group Databasebeta

← Group #225409

Character table — Group #225409

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222444444444444444444444444224444444444888888888888888888888888244488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-11111-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ711111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1711111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1i−ii−i
χ1811111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-1111111-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iii-1-111-1-111−ii−ii
χ1911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−ii−ii
χ2011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-1111111-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i-1-111-1-111i−ii−i
χ2111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-111-1-111−ii−ii
χ2211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111iiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-111ii−i−i−i−iii−i−iii−i−iii−i−iii11-1-111-1-1i−ii−i
χ2311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-111-1-111i−ii−i
χ2411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-111−i−iiiii−i−iii−i−iii−i−iii−i−i11-1-111-1-1−ii−ii
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-11-11−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111iiii−i−i−i−i-1-1-1-111111111-1-1-1-1-11-11−i−iii−i−iii−i−iiiii−i−iii−i−i-1-11111-1-1−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-11-11ii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-11-11ii−i−iii−i−iii−i−i−i−iii−i−iii-1-11111-1-1i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-111111-11-1−i−iiiii−i−iii−i−i−i−iii−i−iii-1-11111-1-1−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1iiii−i−i−i−i-1-1-1-111111111-1-1-1-11-11-1−i−iiiii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-111111-11-1ii−i−i−i−iii−i−iiiii−i−iii−i−i-1-11111-1-1i−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1−i−i−i−iiiii-1-1-1-111111111-1-1-1-11-11-1ii−i−i−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−iii−i
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χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000002-2-2200000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222000000000000000000000000-222-200000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222-2-222-2-222-2-2000000000000000000000000-2-22200000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-22200000000000000000000000022-2-200000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2220000000000000000000000002-22-200000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222-2-22222-2-2000000000000000000000000-22-2200000000000000000000000000000000
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χ45222-2-22-2-222-2-2-2-222−2i−2i2i2i−2i−2i2i2i000000002-200002-2−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000000000000000i2−i2i2−i2−22−220000
χ46222-2-22-2-222-2-2-2-222−2i−2i2i2i−2i−2i2i2i000000002-200002-2−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000000000000000−i2i2−i2i22−22−20000
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χ52222-2-22-2-2-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000-2200002-2−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000000000000000i2−i2−i2i22−2−220000
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χ5822-22-2-22-22i−2i2i2i−2i−2i2i−2i000000002i2i−2i−2i2-22-20000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3-22-22−2i2i−2i2i00000000000000000000−2ζ2ζ−2ζ32ζ300000000000000000000
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χ6322-22-2-22-2−2i2i−2i−2i2i2i−2i2i00000000−2i−2i2i2i2-22-2000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2-22-2−2i2i−2i2i00000000000000000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ6422-22-2-22-2−2i2i−2i−2i2i2i−2i2i00000000−2i−2i2i2i2-22-2000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ-22-222i−2i2i−2i000000000000000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ652-22-22-22-22i−2i2i−2i2i−2i−2i2i2-22-22i−2i2i−2i2i−2i2i−2i2-2-22002-22i−2i000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ0000000000000000
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χ672-22-22-22-22i−2i2i−2i2i−2i−2i2i2-22-22i−2i2i−2i−2i2i−2i2i-222-200-22−2i2i0000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ682-22-22-22-22i−2i2i−2i2i−2i−2i2i2-22-22i−2i2i−2i−2i2i−2i2i-222-200-22−2i2i000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ692-22-22-22-22i−2i2i−2i2i−2i−2i2i-22-22−2i2i−2i2i2i−2i2i−2i2-2-2200-22−2i2i000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ0000000000000000
χ702-22-22-22-22i−2i2i−2i2i−2i−2i2i-22-22−2i2i−2i2i2i−2i2i−2i2-2-2200-22−2i2i00000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00002ζ3−2ζ32ζ−2ζ0000000000000000
χ712-22-22-22-22i−2i2i−2i2i−2i−2i2i-22-22−2i2i−2i2i−2i2i−2i2i-222-2002-22i−2i0000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ722-22-22-22-22i−2i2i−2i2i−2i−2i2i-22-22−2i2i−2i2i−2i2i−2i2i-222-2002-22i−2i000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ732-22-22-22-2−2i2i−2i2i−2i2i2i−2i2-22-2−2i2i−2i2i2i−2i2i−2i-222-200-222i−2i0000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ742-22-22-22-2−2i2i−2i2i−2i2i2i−2i2-22-2−2i2i−2i2i2i−2i2i−2i-222-200-222i−2i000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
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χ782-22-22-22-2−2i2i−2i2i−2i2i2i−2i-22-222i−2i2i−2i2i−2i2i−2i-222-2002-2−2i2i000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ792-22-22-22-2−2i2i−2i2i−2i2i2i−2i-22-222i−2i2i−2i−2i2i−2i2i2-2-2200-222i−2i000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000−2ζ2ζ−2ζ32ζ30000000000000000
χ802-22-22-22-2−2i2i−2i2i−2i2i2i−2i-22-222i−2i2i−2i−2i2i−2i2i2-2-2200-222i−2i00000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300002ζ−2ζ2ζ3−2ζ30000000000000000
χ812-2-2-2-2222222-2-22-2-200000000-222-2-2-2220000000000002i−2i−2i2i−2i2i2i−2i000000002-22-22-22-2000000000000000000002i−2i2i−2i000000000000
χ822-2-2-2-2222222-2-22-2-200000000-222-2-2-2220000000000002i−2i−2i2i−2i2i2i−2i00000000-22-22-22-2200000000000000000000−2i2i−2i2i000000000000
χ832-2-2-2-2222222-2-22-2-200000000-222-2-2-222000000000000−2i2i2i−2i2i−2i−2i2i000000002-22-22-22-200000000000000000000−2i2i−2i2i000000000000
χ842-2-2-2-2222222-2-22-2-200000000-222-2-2-222000000000000−2i2i2i−2i2i−2i−2i2i00000000-22-22-22-22000000000000000000002i−2i2i−2i000000000000
χ852-2-2-2-2222-2-2-222-222000000002-2-22-2-2220000000000002-2-222-2-22000000002-22-2-22-22000000000000000000002-2-22000000000000
χ862-2-2-2-2222-2-2-222-222000000002-2-22-2-2220000000000002-2-222-2-2200000000-22-222-22-200000000000000000000-222-2000000000000
χ872-2-2-2-2222-2-2-222-222000000002-2-22-2-222000000000000-222-2-222-2000000002-22-2-22-2200000000000000000000-222-2000000000000
χ882-2-2-2-2222-2-2-222-222000000002-2-22-2-222000000000000-222-2-222-200000000-22-222-22-2000000000000000000002-2-22000000000000
χ8944-44-4-44-44i−4i4i4i−4i−4i4i−4i00000000−4i−4i4i4i-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ9044-44-4-44-4−4i4i−4i−4i4i4i−4i4i000000004i4i−4i−4i-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-44-4-444i−4i−4i−4i4i4i4i−4i0000000000000000000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000000000000
χ9244-4-44-4-444i−4i−4i−4i4i4i4i−4i000000000000000000000000000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000000000000
χ9344-4-44-4-44−4i4i4i4i−4i−4i−4i4i0000000000000000000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000000000000
χ9444-4-44-4-44−4i4i4i4i−4i−4i−4i4i000000000000000000000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000000000000
χ954-444-4-4-444i−4i−4i4i−4i4i−4i4i4i−4i−4i4i-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ964-444-4-4-444i−4i−4i4i−4i4i−4i4i−4i4i4i−4i4-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ974-444-4-4-44−4i4i4i−4i4i−4i4i−4i4i−4i−4i4i4-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-44−4i4i4i−4i4i−4i4i−4i−4i4i4i−4i-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ994-4-4444-4-444-444-4-4-40000000000000000000000000000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ1004-4-4444-4-444-444-4-4-400000000000000000000000000000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ1014-4-4444-4-4-4-44-4-44440000000000000000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ1024-4-4444-4-4-4-44-4-444400000000000000000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000
χ1034-4-4-4-4444444-4-44-4-4000000004-4-4444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4444-4-4-444-44400000000-444-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.