Finite Group Databasebeta

← Group #98780

Character table — Group #98780

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444444444444444444444222244444444444488888888888888888888888888888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ101111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ121111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ1711111-1-111-1-1-1-1-1-11iiiiii−i−i−i−i−i−i1111-1-1-1-1ii−i−i11-1-111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ1811111-1-111-1-1-1-1-1-11iiiiii−i−i−i−i−i−i1111-1-1-1-1ii−i−i11-1-111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ1911111-1-111-1-1-1-1-1-11iiiiii−i−i−i−i−i−i1111-1-1-1-1ii−i−i11-1-111-1-1iiii−i−i−i−i-1-111−i−iii−i−iii-1-111ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ2011111-1-111-1-1-1-1-1-11iiiiii−i−i−i−i−i−i1111-1-1-1-1ii−i−i11-1-111-1-1iiii−i−i−i−i-1-111−i−iii−i−iii-1-111−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ2111111-1-111-1-1-1-1-1-11iiiiii−i−i−i−i−i−i-1-1-1-11111ii−i−i11-1-1-1-111−i−i−i−iiiii11-1-1ii−i−i−i−iii-1-111ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ2211111-1-111-1-1-1-1-1-11iiiiii−i−i−i−i−i−i-1-1-1-11111ii−i−i11-1-1-1-111−i−i−i−iiiii11-1-1ii−i−i−i−iii-1-111−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ2311111-1-111-1-1-1-1-1-11iiiiii−i−i−i−i−i−i-1-1-1-11111ii−i−i11-1-1-1-111−i−i−i−iiiii-1-111−i−iiiii−i−i11-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ2411111-1-111-1-1-1-1-1-11iiiiii−i−i−i−i−i−i-1-1-1-11111ii−i−i11-1-1-1-111−i−i−i−iiiii-1-111−i−iiiii−i−i11-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ2511111-1-111-1-1-1-1-1-11−i−i−i−i−i−iiiiiii1111-1-1-1-1−i−iii11-1-111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ2611111-1-111-1-1-1-1-1-11−i−i−i−i−i−iiiiiii1111-1-1-1-1−i−iii11-1-111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ2711111-1-111-1-1-1-1-1-11−i−i−i−i−i−iiiiiii1111-1-1-1-1−i−iii11-1-111-1-1−i−i−i−iiiii-1-111ii−i−iii−i−i-1-111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ2811111-1-111-1-1-1-1-1-11−i−i−i−i−i−iiiiiii1111-1-1-1-1−i−iii11-1-111-1-1−i−i−i−iiiii-1-111ii−i−iii−i−i-1-111−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ2911111-1-111-1-1-1-1-1-11−i−i−i−i−i−iiiiiii-1-1-1-11111−i−iii11-1-1-1-111iiii−i−i−i−i11-1-1−i−iiiii−i−i-1-111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ3011111-1-111-1-1-1-1-1-11−i−i−i−i−i−iiiiiii-1-1-1-11111−i−iii11-1-1-1-111iiii−i−i−i−i11-1-1−i−iiiii−i−i-1-111−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ3111111-1-111-1-1-1-1-1-11−i−i−i−i−i−iiiiiii-1-1-1-11111−i−iii11-1-1-1-111iiii−i−i−i−i-1-111ii−i−i−i−iii11-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ3211111-1-111-1-1-1-1-1-11−i−i−i−i−i−iiiiiii-1-1-1-11111−i−iii11-1-1-1-111iiii−i−i−i−i-1-111ii−i−i−i−iii11-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
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χ352222222222222222-2-2-2222-2-2-222222222222-22-22-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000000
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χ752-2-22222-2-2-2-222-2-222i−2i2i0002i−2i−2i000-22-22-22-22−2i02i000000000−2i2i00−2i2i00000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ762-2-22222-2-2-2-222-2-222i−2i2i0002i−2i−2i000-22-22-22-22−2i02i000000000−2i2i00−2i2i0000000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ772-2-22222-2-2-2-222-2-22−2i2i−2i000−2i2i2i0002-22-22-22-22i0−2i000000000−2i2i00−2i2i00000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ782-2-22222-2-2-2-222-2-22−2i2i−2i000−2i2i2i0002-22-22-22-22i0−2i000000000−2i2i00−2i2i0000000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ792-2-22222-2-2-2-222-2-22−2i2i−2i000−2i2i2i000-22-22-22-222i0−2i0000000002i−2i002i−2i00000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ802-2-22222-2-2-2-222-2-22−2i2i−2i000−2i2i2i000-22-22-22-222i0−2i0000000002i−2i002i−2i0000000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ812-2-222-2-2-2-222-2-22222-22000-2220002-22-2-22-22-20-20000000002-200-220000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2
χ822-2-222-2-2-2-222-2-22222-22000-2220002-22-2-22-22-20-20000000002-200-220000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2
χ832-2-222-2-2-2-222-2-22222-22000-222000-22-222-22-2-20-2000000000-22002-20000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2
χ842-2-222-2-2-2-222-2-22222-22000-222000-22-222-22-2-20-2000000000-22002-20000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2
χ852-2-222-2-2-2-222-2-2222-22-20002-2-20002-22-2-22-22202000000000-22002-200000000000000000000000000000000002−2−22−222−22−2−22−222−2
χ862-2-222-2-2-2-222-2-2222-22-20002-2-20002-22-2-22-22202000000000-22002-20000000000000000000000000000000000−222−22−2−22−222−22−2−22
χ872-2-222-2-2-2-222-2-2222-22-20002-2-2000-22-222-22-22020000000002-200-2200000000000000000000000000000000002−2−22−222−2−222−22−2−22
χ882-2-222-2-2-2-222-2-2222-22-20002-2-2000-22-222-22-22020000000002-200-220000000000000000000000000000000000−222−22−2−222−2−22−222−2
χ8944-4-444-4-444-4-44-44-40004i−4i−4i0004i−4i4i0000000004i0−4i0000000000000000000000000000000000000000000000000000000000000000
χ9044-4-444-4-444-4-44-44-4000−4i4i4i000−4i4i−4i000000000−4i04i0000000000000000000000000000000000000000000000000000000000000000
χ9144-4-44-44-44-444-44-4-40004-4-4000-44-40000000004040000000000000000000000000000000000000000000000000000000000000000
χ9244-4-44-44-44-444-44-4-4000-4440004-44000000000-40-40000000000000000000000000000000000000000000000000000000000000000
χ934-444-44-4-44-444-4-44-44i−4i−4i0004i−4i4i000000000004i0−4i00000000000000000000000000000000000000000000000000000000000000000
χ944-444-44-4-44-444-4-44-4−4i4i4i000−4i4i−4i00000000000−4i04i00000000000000000000000000000000000000000000000000000000000000000
χ954-444-4-44-444-4-444-4-44-4-4000-44-40000000000040400000000000000000000000000000000000000000000000000000000000000000
χ964-444-4-44-444-4-444-4-4-4440004-4400000000000-40-400000000000000000000000000000000000000000000000000000000000000000
χ974-44-444-44-4-44-444-4-400000000000000000000000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ984-44-444-44-4-44-444-4-40000000000000000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ994-44-44-444-44-44-4-44-400000000000000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ1004-44-44-444-44-44-4-44-40000000000000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ1014-4-4-4-44444-4-4-4-44440000000000004-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-4-44444-4-4-4-4444000000000000-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-4-4-4-4444444-4-440000000000004-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4-4-4444444-4-44000000000000-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000

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