Finite Group Databasebeta

← Group #357521

Character table — Group #357521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222444444442222222222224444444444448888888888888888222222224444444444444444888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111
χ91111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ121111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ131111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ141111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ151111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ161111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1711111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i111111-1-1-1-1-1-1-1-111ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1811111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i1111-1-111-1-1-1-111-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ1911111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111-1-11111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ2011111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-111111111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ2111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii111111-1-1-1-1-1-1-1-111−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ2211111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii1111-1-111-1-1-1-111-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ2311111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111-1-11111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ2411111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-111111111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii11-1-11111-1-111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1-1-1-1-1111111−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii-1-111111111-1-1-1-1-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-111-1-11111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i11-1-11111-1-111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1-1-1-1-1111111ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i-1-111111111-1-1-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-111-1-11111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ332222222222222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-222-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-22-2-2-222222222-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-22-2-2-222222222-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ41222-2-2-2-222222-2-2-2-222-222-2-222-2-2-222-222-2-222-2-2-2000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ42222-2-2-2-222222-2-2-2-222-222-2-222-2-2-222-222-2-222-2-2-200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ43222-2-2-2-222222-2-2-2-222-2-2-222-2-222-222-2-2-222-2-222-2000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ44222-2-2-2-222222-2-2-2-222-2-2-222-2-222-222-2-2-222-2-222-200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ45222-2-2-2-222222-2-2-2-2-2-2222-2-2-2-2222-2-22-2-22222-2-22000000000000000000000000000000000000000000000000000000002-22-22-22-2
χ46222-2-2-2-222222-2-2-2-2-2-2222-2-2-2-2222-2-22-2-22222-2-2200000000000000000000000000000000000000000000000000000000-22-22-22-22
χ47222-2-2-2-222222-2-2-2-2-2-22-2-22222-2-22-2-2222-2-2-2-2222000000000000000000000000000000000000000000000000000000002-22-2-22-22
χ48222-2-2-2-222222-2-2-2-2-2-22-2-22222-2-22-2-2222-2-2-2-222200000000000000000000000000000000000000000000000000000000-22-222-22-2
χ49222-2-2-2-22-2-2-2-2222222-222-2-222-2-2-2-2-22-2-222-2-2222000000000000000000000000000000000000000000000000000000002-2-222-2-22
χ50222-2-2-2-22-2-2-2-2222222-222-2-222-2-2-2-2-22-2-222-2-222200000000000000000000000000000000000000000000000000000000-222-2-222-2
χ51222-2-2-2-22-2-2-2-2222222-2-2-222-2-222-2-2-2222-2-222-2-22000000000000000000000000000000000000000000000000000000002-2-22-222-2
χ52222-2-2-2-22-2-2-2-2222222-2-2-222-2-222-2-2-2222-2-222-2-2200000000000000000000000000000000000000000000000000000000-222-22-2-22
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χ582-2-222-2-2222-2-222-2-22-222-22-22-22-2-22-222-22-22-22-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ592-2-222-2-2222-2-222-2-22-22-22-22-22-22-22-22-22-22-22-22-20000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
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χ612-2-222-2-2222-2-222-2-2-22-22-22-2-22-222-22-2-22-222-22-22000000000000000000002-22-200002-22-200000000000000000000000000000000
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χ702-2-222-2-22-2-222-2-222-22-22-22-2-22-2222-222-22-2-22-22-2000000000000000000000000000000000000000000000000-222-2-222-200000000
χ712-2-222-2-22-2-222-2-222-22-2-22-222-22-222-22-22-222-22-2-20000000000000000000000000000000000000000000000002-2-22-222-200000000
χ722-2-222-2-22-2-222-2-222-22-2-22-222-22-222-22-22-222-22-2-2000000000000000000000000000000000000000000000000-222-22-2-2200000000
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χ742-2-2-2-222222-2-2-2-2222-2-22-2-222-2-2222-2-22-2-222-2-2220000000000000000-22-220000-22-22000000000000000000000000000000000000
χ752-2-2-2-222222-2-2-2-2222-2-2-222-2-222-222-2-2-222-2-222-2200000000000000002-2-2200002-2-22000000000000000000000000000000000000
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χ782-2-2-2-222222-2-2-2-222-2222-2-22-222-2-2-222-222-22-2-22-20000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ792-2-2-2-222222-2-2-2-222-222-222-22-2-22-2-2222-2-22-222-2-200000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ802-2-2-2-222222-2-2-2-222-222-222-22-2-22-2-2222-2-22-222-2-20000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
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χ882-2-2-2-2222-2-22222-2-2-222-222-22-2-22-22-2-2-222-22-2-2220000000000000000-222-200002-2-22000000000000000000000000000000000000
χ8944-44-44-4-44i−4i4i−4i4i−4i4i−4i00000000000000000000000000000000004ζ3−4ζ3004ζ−4ζ000000000000000000000000000000000000000000000000
χ9044-44-44-4-44i−4i4i−4i4i−4i4i−4i0000000000000000000000000000000000−4ζ34ζ300−4ζ4ζ000000000000000000000000000000000000000000000000
χ9144-44-44-4-4−4i4i−4i4i−4i4i−4i4i00000000000000000000000000000000004ζ−4ζ004ζ3−4ζ3000000000000000000000000000000000000000000000000
χ9244-44-44-4-4−4i4i−4i4i−4i4i−4i4i0000000000000000000000000000000000−4ζ4ζ00−4ζ34ζ3000000000000000000000000000000000000000000000000
χ9344-4-44-44-44i−4i4i−4i−4i4i−4i4i000000000000000000000000000000004ζ−4ζ004ζ3−4ζ300000000000000000000000000000000000000000000000000
χ9444-4-44-44-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000−4ζ4ζ00−4ζ34ζ300000000000000000000000000000000000000000000000000
χ9544-4-44-44-4−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000004ζ3−4ζ3004ζ−4ζ00000000000000000000000000000000000000000000000000
χ9644-4-44-44-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000−4ζ34ζ300−4ζ4ζ00000000000000000000000000000000000000000000000000
χ974-444-4-44-44i−4i−4i4i4i−4i−4i4i0000000000000000000000004ζ3−4ζ3004ζ−4ζ0000000000000000000000000000000000000000000000000000000000
χ984-444-4-44-44i−4i−4i4i4i−4i−4i4i000000000000000000000000−4ζ34ζ300−4ζ4ζ0000000000000000000000000000000000000000000000000000000000
χ994-444-4-44-4−4i4i4i−4i−4i4i4i−4i0000000000000000000000004ζ−4ζ004ζ3−4ζ30000000000000000000000000000000000000000000000000000000000
χ1004-444-4-44-4−4i4i4i−4i−4i4i4i−4i000000000000000000000000−4ζ4ζ00−4ζ34ζ30000000000000000000000000000000000000000000000000000000000
χ1014-44-444-4-44i−4i−4i4i−4i4i4i−4i000000000000000000000000004ζ−4ζ004ζ3−4ζ300000000000000000000000000000000000000000000000000000000
χ1024-44-444-4-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000−4ζ4ζ00−4ζ34ζ300000000000000000000000000000000000000000000000000000000
χ1034-44-444-4-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000004ζ3−4ζ3004ζ−4ζ00000000000000000000000000000000000000000000000000000000
χ1044-44-444-4-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000−4ζ34ζ300−4ζ4ζ00000000000000000000000000000000000000000000000000000000

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