Finite Group Databasebeta

← Group #92813

Character table — Group #92813

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
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i
χ91111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ101111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii
χ111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ121111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1
χ1711111-1-1-1-1111-1-1-1-1111-1-1-1iii−i−i−iiii−i−i−i1-1i−ii−i11-1-111-1-1ii−i−iii−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
χ1811111-1-1-1-1111-1-1-1-1111-1-1-1iii−i−i−iiii−i−i−i1-1i−ii−i11-1-111-1-1ii−i−iii−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
χ1911111-1-1-1-1111-1-1-1-1111-1-1-1iii−i−i−iiii−i−i−i1-1i−ii−i11-1-111-1-1ii−i−iii−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
χ2011111-1-1-1-1111-1-1-1-1111-1-1-1iii−i−i−iiii−i−i−i1-1i−ii−i11-1-111-1-1ii−i−iii−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
χ2111111-1-1-1-1111-1-1-1-1111-1-1-1−i−i−iiii−i−i−iiii1-1−ii−ii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iiiζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζ
χ2211111-1-1-1-1111-1-1-1-1111-1-1-1−i−i−iiii−i−i−iiii1-1−ii−ii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ
χ2311111-1-1-1-1111-1-1-1-1111-1-1-1−i−i−iiii−i−i−iiii1-1−ii−ii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−iζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ
χ2411111-1-1-1-1111-1-1-1-1111-1-1-1−i−i−iiii−i−i−iiii1-1−ii−ii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζ
χ2511111-1-1-1-1111-1-1-1-1-1-1-1111iii−i−i−i−i−i−iiii-11i−i−ii11-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζ
χ2611111-1-1-1-1111-1-1-1-1-1-1-1111iii−i−i−i−i−i−iiii-11i−i−ii11-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ
χ2711111-1-1-1-1111-1-1-1-1-1-1-1111iii−i−i−i−i−i−iiii-11i−i−ii11-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ
χ2811111-1-1-1-1111-1-1-1-1-1-1-1111iii−i−i−i−i−i−iiii-11i−i−ii11-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζ
χ2911111-1-1-1-1111-1-1-1-1-1-1-1111−i−i−iiiiiii−i−i−i-11−iii−i11-1-1-1-111−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3
χ3011111-1-1-1-1111-1-1-1-1-1-1-1111−i−i−iiiiiii−i−i−i-11−iii−i11-1-1-1-111−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3
χ3111111-1-1-1-1111-1-1-1-1-1-1-1111−i−i−iiiiiii−i−i−i-11−iii−i11-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3
χ3211111-1-1-1-1111-1-1-1-1-1-1-1111−i−i−iiiiiii−i−i−i-11−iii−i11-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3
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χ742-22-222-22-2-22-2-22-222-222-222-222-22000000-2-2-2-2000000000000002-22-200000000000000000000000000000000−22−22−22−22−22−22−22−22
χ752-22-222-22-2-22-2-22-222-222-22-22-2-22-2000000-2-22200000000000000-22-2200000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2
χ762-22-222-22-2-22-2-22-222-222-22-22-2-22-2000000-2-22200000000000000-22-2200000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2
χ772-22-222-22-2-22-2-22-22-22-2-22-22-222-2200000022-2-200000000000000-22-2200000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2
χ782-22-222-22-2-22-2-22-22-22-2-22-22-222-2200000022-2-200000000000000-22-2200000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2
χ792-22-222-22-2-22-2-22-22-22-2-22-2-22-2-22-20000002222000000000000002-22-2000000000000000000000000000000002−22−2−22−22−22−222−22−2
χ802-22-222-22-2-22-2-22-22-22-2-22-2-22-2-22-20000002222000000000000002-22-200000000000000000000000000000000−22−222−22−22−22−2−22−22
χ812-22-22-22-22-22-22-22-22-22-22-22i−2i2i−2i2i−2i000000-22−2i2i000000000000002i−2i−2i2i000000000000000000000000000000001+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i
χ822-22-22-22-22-22-22-22-22-22-22-22i−2i2i−2i2i−2i000000-22−2i2i000000000000002i−2i−2i2i00000000000000000000000000000000−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i
χ832-22-22-22-22-22-22-22-22-22-22-2−2i2i−2i2i−2i2i000000-222i−2i00000000000000−2i2i2i−2i000000000000000000000000000000001−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i
χ842-22-22-22-22-22-22-22-22-22-22-2−2i2i−2i2i−2i2i000000-222i−2i00000000000000−2i2i2i−2i00000000000000000000000000000000−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i
χ852-22-22-22-22-22-22-22-2-22-22-222i−2i2i−2i2i−2i0000002-2−2i2i00000000000000−2i2i2i−2i000000000000000000000000000000001−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i
χ862-22-22-22-22-22-22-22-2-22-22-222i−2i2i−2i2i−2i0000002-2−2i2i00000000000000−2i2i2i−2i00000000000000000000000000000000−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i
χ872-22-22-22-22-22-22-22-2-22-22-22−2i2i−2i2i−2i2i0000002-22i−2i000000000000002i−2i−2i2i000000000000000000000000000000001+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i
χ882-22-22-22-22-22-22-22-2-22-22-22−2i2i−2i2i−2i2i0000002-22i−2i000000000000002i−2i−2i2i00000000000000000000000000000000−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i
χ8944-4-444-4-44-4-444-4-440000000000004-4-44-4-40000440000000000000000000000000000000000000000000000000000000000000000
χ9044-4-444-4-44-4-444-4-44000000000000-444-4440000-4-40000000000000000000000000000000000000000000000000000000000000000
χ9144-4-44-444-4-4-44-444-40000000000004i−4i−4i−4i4i4i00004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ9244-4-44-444-4-4-44-444-4000000000000−4i4i4i4i−4i−4i0000−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ934-444-44-4-44-4-44-444-40000004-4-44-4-40000000044000000000000000000000000000000000000000000000000000000000000000000
χ944-444-44-4-44-4-44-444-4000000-444-44400000000-4-4000000000000000000000000000000000000000000000000000000000000000000
χ954-444-4-444-4-4-444-4-440000004i−4i−4i−4i4i4i000000004i−4i000000000000000000000000000000000000000000000000000000000000000000
χ964-444-4-444-4-4-444-4-44000000−4i4i4i4i−4i−4i00000000−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ974-4-44444-4-44-4-4-4-4440000000000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ984-4-44444-4-44-4-4-4-444000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ994-4-444-4-4444-4-444-4-40000000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ1004-4-444-4-4444-4-444-4-4000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ1014-4-4-4-44444444-4-4-4-44-4-44-4-40000000000004400000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-4-44444444-4-4-4-4-444-444000000000000-4-400000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-4-4-4-4-4-444444444-4-4-4440000000000004-400000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4-4-4-4-44444444-4444-4-4000000000000-4400000000000000000000000000000000000000000000000000000000000000000000

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