Finite Group Databasebeta

← Group #96916

Character table — Group #96916

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444442222444444444444444444444444444488888888888888888888888888888888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i
χ91111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ1711111-1-1-1-1-1-1111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3
χ1811111-1-1-1-1-1-1111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3
χ1911111-1-1-1-1-1-1111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i-1-111-1-111−i−iii−i−iiiζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3
χ2011111-1-1-1-1-1-1111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i-1-111-1-111−i−iii−i−iii−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3
χ2111111-1-1-1-1-1-1111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iiiζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζ
χ2211111-1-1-1-1-1-1111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ
χ2311111-1-1-1-1-1-1111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii-1-111-1-111ii−i−iii−i−iζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ
χ2411111-1-1-1-1-1-1111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζ
χ2511111-1-1-1-1-1-1111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iiiζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3
χ2611111-1-1-1-1-1-1111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3
χ2711111-1-1-1-1-1-1111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−iζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3
χ2811111-1-1-1-1-1-1111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3
χ2911111-1-1-1-1-1-1111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1iiii−i−i−i−i11-1-1-1-111−i−iiiii−i−iζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζ
χ3011111-1-1-1-1-1-1111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1iiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ
χ3111111-1-1-1-1-1-1111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iiiζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ
χ3211111-1-1-1-1-1-1111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζ
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χ34222222222222222222222222-2-222-2-222-2-222-2-222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-22222-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000000
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χ6822-22-2-2-22-222-22-22-22i−2i2i−2i−2i2i−2i2i-22002-200-22002-200000000002i−2i00−2i2i0000000000000000000000000000000000−222−2−i2i2i2−i22−2−22−i2i2i2−i2
χ6922-22-2-2-22-222-22-22-2−2i2i−2i2i2i−2i2i−2i2-200-22002-200-2200000000002i−2i00−2i2i0000000000000000000000000000000000i2−i2−i2i22−2−22i2−i2−i2i2−222−2
χ7022-22-2-2-22-222-22-22-2−2i2i−2i2i2i−2i2i−2i2-200-22002-200-2200000000002i−2i00−2i2i0000000000000000000000000000000000−i2i2i2−i2−222−2−i2i2i2−i22−2−22
χ7122-22-2-2-22-222-22-22-2−2i2i−2i2i2i−2i2i−2i-22002-200-22002-20000000000−2i2i002i−2i00000000000000000000000000000000002−2−22−i2i2i2−i2−222−2−i2i2i2−i2
χ7222-22-2-2-22-222-22-22-2−2i2i−2i2i2i−2i2i−2i-22002-200-22002-20000000000−2i2i002i−2i0000000000000000000000000000000000−222−2i2−i2−i2i22−2−22i2−i2−i2i2
χ732-2-2-2-22-2222-2222-2-2000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00002-22-2000000002-22-200002i−2i2i−2i000000000000000000000000000000000000
χ742-2-2-2-22-2222-2222-2-2000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00002-22-200000000-22-220000−2i2i−2i2i000000000000000000000000000000000000
χ752-2-2-2-22-2222-2222-2-2000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i0000-22-220000000000002-22-200002i−2i2i−2i00000000000000000000000000000000
χ762-2-2-2-22-2222-2222-2-2000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i0000-22-22000000000000-22-220000−2i2i−2i2i00000000000000000000000000000000
χ772-2-2-2-22-2222-2222-2-200000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000-22-220000000000002-22-20000−2i2i−2i2i00000000000000000000000000000000
χ782-2-2-2-22-2222-2222-2-200000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000-22-22000000000000-22-2200002i−2i2i−2i00000000000000000000000000000000
χ792-2-2-2-22-2222-2222-2-200000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00002-22-2000000002-22-20000−2i2i−2i2i000000000000000000000000000000000000
χ802-2-2-2-22-2222-2222-2-200000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00002-22-200000000-22-2200002i−2i2i−2i000000000000000000000000000000000000
χ812-2-2-2-2-22-2-2-2222222000000002-22-2-22-22-22-222-22-200002-2-22000000002-2-2200002-2-22000000000000000000000000000000000000
χ822-2-2-2-2-22-2-2-2222222000000002-22-2-22-22-22-222-22-200002-2-2200000000-222-20000-222-2000000000000000000000000000000000000
χ832-2-2-2-2-22-2-2-2222222000000002-2-22-222-2-222-22-2-220000-222-20000000000002-2-2200002-2-2200000000000000000000000000000000
χ842-2-2-2-2-22-2-2-2222222000000002-2-22-222-2-222-22-2-220000-222-2000000000000-222-20000-222-200000000000000000000000000000000
χ852-2-2-2-2-22-2-2-222222200000000-222-22-2-222-2-22-222-20000-222-20000000000002-2-220000-222-200000000000000000000000000000000
χ862-2-2-2-2-22-2-2-222222200000000-222-22-2-222-2-22-222-20000-222-2000000000000-222-200002-2-2200000000000000000000000000000000
χ872-2-2-2-2-22-2-2-222222200000000-22-222-22-22-22-2-22-2200002-2-22000000002-2-220000-222-2000000000000000000000000000000000000
χ882-2-2-2-2-22-2-2-222222200000000-22-222-22-22-22-2-22-2200002-2-2200000000-222-200002-2-22000000000000000000000000000000000000
χ8944-4-4444-4-444-4-44-4-44-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9044-4-4444-4-444-4-44-4-4-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-44-4-444-4-4-4-44444-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9244-4-44-4-444-4-4-4-4444-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ934-444-44-4-4-44-4-4-44440000000000000000000000004-44-4000000000000000000000000000000000000000000000000000000000000
χ944-444-44-4-4-44-4-4-4444000000000000000000000000-44-44000000000000000000000000000000000000000000000000000000000000
χ954-444-4-4444-44-4-44-4-40000000000000000000000004-4-44000000000000000000000000000000000000000000000000000000000000
χ964-444-4-4444-44-4-44-4-4000000000000000000000000-444-4000000000000000000000000000000000000000000000000000000000000
χ974-44-444-4-44-44-44-44-40000000044004400-4-400-4-4000000000000000000000000000000000000000000000000000000000000000000
χ984-44-444-4-44-44-44-44-400000000-4-400-4-400440044000000000000000000000000000000000000000000000000000000000000000000
χ994-44-44-444-44-4-44-4-44000000004i4i00−4i−4i00−4i−4i004i4i000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-44-444-44-4-44-4-4400000000−4i−4i004i4i004i4i00−4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-4444-44-4-444-4-4-44000000000044004400-4-400-4-40000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4444-44-4-444-4-4-440000000000-4-400-4-4004400440000000000000000000000000000000000000000000000000000000000000000
χ1034-4-444-44-444-44-4-44-400000000004i4i00−4i−4i00−4i−4i004i4i0000000000000000000000000000000000000000000000000000000000000000
χ1044-4-444-44-444-44-4-44-40000000000−4i−4i004i4i004i4i00−4i−4i0000000000000000000000000000000000000000000000000000000000000000

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