Finite Group Databasebeta

← Group #92809

Character table — Group #92809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444444444444444444444888888888888888888888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1
χ91111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ101111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ121111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ141111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii
χ151111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ161111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i
χ1711111-1-1-1-1111-1-1-1-1iii−i−i−i11-1-1ii−i−i11-1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ1811111-1-1-1-1111-1-1-1-1iii−i−i−i11-1-1ii−i−i11-1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ1911111-1-1-1-1111-1-1-1-1iii−i−i−i11-1-1ii−i−i11-1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iiiζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ2011111-1-1-1-1111-1-1-1-1iii−i−i−i11-1-1ii−i−i11-1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ2111111-1-1-1-1111-1-1-1-1iii−i−i−i-1-111−i−iii-1-111−i−iiii−i11-1-1ii−i−i-1-111−i−iiiii−i−i-1-111−i−iii11-1-1ζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ2211111-1-1-1-1111-1-1-1-1iii−i−i−i-1-111−i−iii-1-111−i−iiii−i11-1-1ii−i−i-1-111−i−iiiii−i−i-1-111−i−iii11-1-1−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ2311111-1-1-1-1111-1-1-1-1iii−i−i−i-1-111−i−iii-1-111−i−iiii−i11-1-1ii−i−i-1-111−i−iii−i−iii11-1-1ii−i−i-1-111ζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ2411111-1-1-1-1111-1-1-1-1iii−i−i−i-1-111−i−iii-1-111−i−iiii−i11-1-1ii−i−i-1-111−i−iii−i−iii11-1-1ii−i−i-1-111−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ2511111-1-1-1-1111-1-1-1-1−i−i−iiii11-1-1−i−iii11-1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ2611111-1-1-1-1111-1-1-1-1−i−i−iiii11-1-1−i−iii11-1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ2711111-1-1-1-1111-1-1-1-1−i−i−iiii11-1-1−i−iii11-1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ2811111-1-1-1-1111-1-1-1-1−i−i−iiii11-1-1−i−iii11-1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ2911111-1-1-1-1111-1-1-1-1−i−i−iiii-1-111ii−i−i-1-111ii−i−i−ii11-1-1−i−iii-1-111ii−i−iii−i−i11-1-1−i−iii-1-111ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ3011111-1-1-1-1111-1-1-1-1−i−i−iiii-1-111ii−i−i-1-111ii−i−i−ii11-1-1−i−iii-1-111ii−i−iii−i−i11-1-1−i−iii-1-111−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ3111111-1-1-1-1111-1-1-1-1−i−i−iiii-1-111ii−i−i-1-111ii−i−i−ii11-1-1−i−iii-1-111ii−i−i−i−iii-1-111ii−i−i11-1-1ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ3211111-1-1-1-1111-1-1-1-1−i−i−iiii-1-111ii−i−i-1-111ii−i−i−ii11-1-1−i−iii-1-111ii−i−i−i−iii-1-111ii−i−i11-1-1−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
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χ342222222222222222222222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-22222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222000000000000000000000000000000000000000000000000
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χ52222-2-2-2-2222-2-2-2-2220000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000002-2-220000000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i22−2−22−222−2
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χ742-2-22222-2-22-2-2-2-2222i−2i2i2i−2i−2i00002i2i−2i−2i0000−2i−2i2i2i−2i2i000000002-22-20000−22−22−i2i2−i2i2−22−22−i2i2−i2i200000000000000000000000000000000
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χ762-2-22222-2-22-2-2-2-2222i−2i2i2i−2i−2i0000−2i−2i2i2i00002i2i−2i−2i−2i2i00000000-22-220000−i2i2−i2i22−22−2i2−i2i2−i2−22−2200000000000000000000000000000000
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χ822-2-222-2-2222-2-222-2-22-22-222000022220000-2-2-2-2-2-2000000002-2-220000−222−2−222−2−222−2−222−200000000000000000000000000000000
χ832-2-222-2-2222-2-222-2-22-22-2220000-2-2-2-200002222-2-200000000-222-20000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000000000000000000000000000
χ842-2-222-2-2222-2-222-2-22-22-2220000-2-2-2-200002222-2-200000000-222-20000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000000000000000000000000000
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χ862-2-222-2-2222-2-222-2-2-22-22-2-2000022220000-2-2-2-22200000000-222-20000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000000000000000000000000
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χ882-2-222-2-2222-2-222-2-2-22-22-2-20000-2-2-2-20000222222000000002-2-220000−222−22−2−22−222−22−2−2200000000000000000000000000000000
χ8944-4-444-4-44-4-444-4-440000004i−4i4i−4i0000−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ9044-4-444-4-44-4-444-4-44000000−4i4i−4i4i00004i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-44-444-4-4-44-444-40000004i−4i−4i4i0000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ9244-4-44-444-4-4-44-444-4000000−4i4i4i−4i00004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ934-444-44-4-44-4-44-444-44i−4i−4i4i−4i4i00000000000000004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ944-444-44-4-44-4-44-444-4−4i4i4i−4i4i−4i0000000000000000−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ954-444-4-444-4-4-444-4-444-4-4-44-40000000000000000440000000000000000000000000000000000000000000000000000000000000000
χ964-444-4-444-4-4-444-4-44-4444-440000000000000000-4-40000000000000000000000000000000000000000000000000000000000000000
χ974-44-444-44-4-44-4-44-440000000000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ984-44-444-44-4-44-4-44-44000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ994-44-44-44-44-44-44-44-40000000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ1004-44-44-44-44-44-44-44-4000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ1014-4-4-4-44444444-4-4-4-400000000004i−4i−4i4i0000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-4-44444444-4-4-4-40000000000−4i4i4i−4i00004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-4-4-4-4-4-4444444400000000004-44-40000-44-44000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4-4-4-4-444444440000000000-44-4400004-44-4000000000000000000000000000000000000000000000000000000000000000000

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