Finite Group Databasebeta

← Group #210821

Character table — Group #210821

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444444444444488888888888888882244444488888888888888888888888888888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-111-1-111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1111-1-1-11111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1111-1-1-1111-1-1-1-111
χ9111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ10111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-111-1-11-1-1-111-1-111
χ12111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-1-111-1111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-1-1111-111-1-1-1-111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1111-1-1-11-1-11111-1-1
χ1711111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i111-11-1-1-1i−ii−ii−ii−i
χ1811111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-11-1111−ii−ii−ii−ii
χ1911111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii1-11-1-11-11i−i−iii−i−ii
χ2011111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-11-111-11-1−iii−i−iii−i
χ2111111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-11-11-1-1−ii−iii−ii−i
χ2211111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-11-11-111i−ii−i−ii−ii
χ2311111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i1-1-111-1-11−iii−ii−i−ii
χ2411111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-111-1-111-1i−i−ii−iii−i
χ2511111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii111-11-1-1-1−ii−ii−ii−ii
χ2611111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-1-11-1111i−ii−ii−ii−i
χ2711111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i1-11-1-11-11−iii−i−iii−i
χ2811111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-11-111-11-1i−i−iii−i−ii
χ2911111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-11-11-1-1i−ii−i−ii−ii
χ3011111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-11-11-111−ii−iii−ii−i
χ3111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii1-1-111-1-11i−i−ii−iii−i
χ3211111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-111-1-111-1−iii−ii−i−ii
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χ7722-2-2-2-22222-2-222-2-2-2-22222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000002-2-222-2-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ7822-2-2-2-22222-2-222-2-2-2-22222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000-222-2-222-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ7922-2-2-2-22222-2-222-2-2-2-22222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000002-2-222-2-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ8022-2-2-2-22222-2-222-2-2-2-22222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000-222-2-222-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ8122-2-2-2-222-2-222-2-2222222-2-2-2-222-2-2-2-22222-2-2-2-222000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000
χ8222-2-2-2-222-2-222-2-2222222-2-2-2-222-2-2-2-22222-2-2-2-22200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000000
χ8322-2-2-2-222-2-222-2-2222222-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000
χ8422-2-2-2-222-2-222-2-2222222-2-2-2-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000
χ8522-2-2-2-222-2-222-2-222-2-2-2-2222222-2-2-2-222-2-22222-2-200000000000000002-2-22-222-2-222-2-222-200000000000000000000000000000000
χ8622-2-2-2-222-2-222-2-222-2-2-2-2222222-2-2-2-222-2-22222-2-20000000000000000-222-22-2-222-2-222-2-2200000000000000000000000000000000
χ8722-2-2-2-222-2-222-2-222-2-2-2-22222-2-22222-2-222-2-2-2-22200000000000000002-2-22-222-22-2-222-2-2200000000000000000000000000000000
χ8822-2-2-2-222-2-222-2-222-2-2-2-22222-2-22222-2-222-2-2-2-2220000000000000000-222-22-2-22-222-2-222-200000000000000000000000000000000
χ894-44-44-44-44i−4i4i−4i4i−4i−4i4i000000004ζ−4ζ4ζ−4ζ4ζ3−4ζ34ζ3−4ζ3000000000000000000000000000000000000000000000000000000000000000000000000
χ904-44-44-44-44i−4i4i−4i4i−4i−4i4i00000000−4ζ4ζ−4ζ4ζ−4ζ34ζ3−4ζ34ζ3000000000000000000000000000000000000000000000000000000000000000000000000
χ914-44-44-44-4−4i4i−4i4i−4i4i4i−4i000000004ζ3−4ζ34ζ3−4ζ34ζ−4ζ4ζ−4ζ000000000000000000000000000000000000000000000000000000000000000000000000
χ924-44-44-44-4−4i4i−4i4i−4i4i4i−4i00000000−4ζ34ζ3−4ζ34ζ3−4ζ4ζ−4ζ4ζ000000000000000000000000000000000000000000000000000000000000000000000000
χ934-44-4-44-444-444-44-4-400000000000000004i−4i4i−4i4i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ944-44-4-44-444-444-44-4-40000000000000000−4i4i−4i4i−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ954-44-4-44-44-44-4-44-44400000000000000004-44-4-44-440000000000000000000000000000000000000000000000000000000000000000
χ964-44-4-44-44-44-4-44-4440000000000000000-44-444-44-40000000000000000000000000000000000000000000000000000000000000000
χ974-4-444-4-444-4-4-4-444400000000000000004-4-444-4-440000000000000000000000000000000000000000000000000000000000000000
χ984-4-444-4-444-4-4-4-44440000000000000000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000
χ994-4-444-4-44-44444-4-4-400000000000000004i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ1004-4-444-4-44-44444-4-4-40000000000000000−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-444-44i−4i−4i4i4i−4i4i−4i000000004ζ3−4ζ3−4ζ34ζ3−4ζ4ζ4ζ−4ζ000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-44-444-44i−4i−4i4i4i−4i4i−4i00000000−4ζ34ζ34ζ3−4ζ34ζ−4ζ−4ζ4ζ000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-444-4−4i4i4i−4i−4i4i−4i4i000000004ζ−4ζ−4ζ4ζ−4ζ34ζ34ζ3−4ζ3000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-444-4−4i4i4i−4i−4i4i−4i4i00000000−4ζ4ζ4ζ−4ζ4ζ3−4ζ3−4ζ34ζ3000000000000000000000000000000000000000000000000000000000000000000000000

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