Finite Group Databasebeta

← Group #98792

Character table — Group #98792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444444444444444444444444444444444444488888888888888888888888888888888
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
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ101111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ121111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ171111-1-1-111-1-1-11-11-1iiiii−i−i−i−i−iiiii−i−i−i−iii−i−ii−i1111-1-1-1-111-1-1ii−i−i11-1-1ii−i−iii−i−i11-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ181111-1-1-111-1-1-11-11-1iiiii−i−i−i−i−iiiii−i−i−i−iii−i−ii−i1111-1-1-1-111-1-1ii−i−i11-1-1ii−i−iii−i−i11-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ191111-1-1-111-1-1-11-11-1iiiii−i−i−i−i−iiiii−i−i−i−iii−i−ii−i1111-1-1-1-111-1-1ii−i−i-1-111−i−iii−i−iii-1-111ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ201111-1-1-111-1-1-11-11-1iiiii−i−i−i−i−iiiii−i−i−i−iii−i−ii−i1111-1-1-1-111-1-1ii−i−i-1-111−i−iii−i−iii-1-111−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ211111-1-1-111-1-1-11-11-1iiiii−i−i−i−i−i−i−i−i−iiiiiii−i−ii−i-1-1-1-1111111-1-1−i−iii11-1-1−i−iiiii−i−i-1-111ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ221111-1-1-111-1-1-11-11-1iiiii−i−i−i−i−i−i−i−i−iiiiiii−i−ii−i-1-1-1-1111111-1-1−i−iii11-1-1−i−iiiii−i−i-1-111−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ231111-1-1-111-1-1-11-11-1iiiii−i−i−i−i−i−i−i−i−iiiiiii−i−ii−i-1-1-1-1111111-1-1−i−iii-1-111ii−i−i−i−iii11-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ241111-1-1-111-1-1-11-11-1iiiii−i−i−i−i−i−i−i−i−iiiiiii−i−ii−i-1-1-1-1111111-1-1−i−iii-1-111ii−i−i−i−iii11-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ251111-1-1-111-1-1-11-11-1−i−i−i−i−iiiiiiiiii−i−i−i−i−i−iii−ii-1-1-1-1111111-1-1ii−i−i11-1-1ii−i−i−i−iii-1-111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ261111-1-1-111-1-1-11-11-1−i−i−i−i−iiiiiiiiii−i−i−i−i−i−iii−ii-1-1-1-1111111-1-1ii−i−i11-1-1ii−i−i−i−iii-1-111−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ271111-1-1-111-1-1-11-11-1−i−i−i−i−iiiiiiiiii−i−i−i−i−i−iii−ii-1-1-1-1111111-1-1ii−i−i-1-111−i−iiiii−i−i11-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ281111-1-1-111-1-1-11-11-1−i−i−i−i−iiiiiiiiii−i−i−i−i−i−iii−ii-1-1-1-1111111-1-1ii−i−i-1-111−i−iiiii−i−i11-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ291111-1-1-111-1-1-11-11-1−i−i−i−i−iiiiii−i−i−i−iiiii−i−iii−ii1111-1-1-1-111-1-1−i−iii11-1-1−i−iii−i−iii11-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ301111-1-1-111-1-1-11-11-1−i−i−i−i−iiiiii−i−i−i−iiiii−i−iii−ii1111-1-1-1-111-1-1−i−iii11-1-1−i−iii−i−iii11-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ311111-1-1-111-1-1-11-11-1−i−i−i−i−iiiiii−i−i−i−iiiii−i−iii−ii1111-1-1-1-111-1-1−i−iii-1-111ii−i−iii−i−i-1-111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ321111-1-1-111-1-1-11-11-1−i−i−i−i−iiiiii−i−i−i−iiiii−i−iii−ii1111-1-1-1-111-1-1−i−iii-1-111ii−i−iii−i−i-1-111−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3
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χ382222-2-2-222-2-2-22-22-22i2i2i−2i−2i−2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i2i−2i-2-22222-2-2-2-2222i2i−2i−2i000000000000000000000000000000000000000000000000
χ392222-2-2-222-2-2-22-22-2−2i−2i−2i2i2i2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i−2i−2i−2i2i-2-22222-2-2-2-222−2i−2i2i2i000000000000000000000000000000000000000000000000
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χ6322-222-22-2-22-2-2-2-222−2i2i−2i−2i−2i−2i2i2i2i2i000000002i2i−2i−2i2i−2i000000002-22-2000000002i−2i2i−2i0000-22-2200000000000000000000000000000000
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χ772-2-2222-22-2-2-222-2-22000-22000-222i−2i2i−2i2i−2i2i−2i-22-220000−2i2i00−2i2i0000000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−2
χ782-2-2222-22-2-2-222-2-22000-22000-222i−2i2i−2i2i−2i2i−2i-22-220000−2i2i00−2i2i0000000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−22
χ792-2-2222-22-2-2-222-2-22000-22000-22−2i2i−2i2i−2i2i−2i2i-22-2200002i−2i002i−2i0000000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−22
χ802-2-2222-22-2-2-222-2-22000-22000-22−2i2i−2i2i−2i2i−2i2i-22-2200002i−2i002i−2i0000000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−2
χ812-2-22-2-222-222-222-2-20002i−2i000−2i2i2-22-2-22-222i−2i−2i2i0000−2i2i002i−2i00000000000000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ822-2-22-2-222-222-222-2-20002i−2i000−2i2i2-22-2-22-222i−2i−2i2i0000−2i2i002i−2i0000000000000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ832-2-22-2-222-222-222-2-20002i−2i000−2i2i-22-222-22-22i−2i−2i2i00002i−2i00−2i2i00000000000000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ842-2-22-2-222-222-222-2-20002i−2i000−2i2i-22-222-22-22i−2i−2i2i00002i−2i00−2i2i0000000000000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i
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χ862-2-22-2-222-222-222-2-2000−2i2i0002i−2i2-22-2-22-22−2i2i2i−2i00002i−2i00−2i2i0000000000000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ872-2-22-2-222-222-222-2-2000−2i2i0002i−2i-22-222-22-2−2i2i2i−2i0000−2i2i002i−2i00000000000000000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ882-2-22-2-222-222-222-2-2000−2i2i0002i−2i-22-222-22-2−2i2i2i−2i0000−2i2i002i−2i0000000000000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ8944-4-44-4-4-444-4444-4-44i−4i−4i004i−4i4i000000000000004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ9044-4-44-4-4-444-4444-4-4−4i4i4i00−4i4i−4i00000000000000−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ9144-4-4-444-44-44-44-4-444-4-400-44-400000000000000440000000000000000000000000000000000000000000000000000000000000000
χ9244-4-4-444-44-44-44-4-44-444004-4400000000000000-4-40000000000000000000000000000000000000000000000000000000000000000
χ934-4444-4-4-44-44-4-44-440004i−4i000−4i4i00000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ944-4444-4-4-44-44-4-44-44000−4i4i0004i−4i000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ954-444-444-444-44-4-4-4-40004-40004-400000000-44-44000000000000000000000000000000000000000000000000000000000000000000
χ964-444-444-444-44-4-4-4-4000-44000-44000000004-44-4000000000000000000000000000000000000000000000000000000000000000000
χ974-44-44-44-4-4-4444-44-40000000000000000000000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ984-44-44-44-4-4-4444-44-4000000000000000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ994-44-4-44-4-4-44-4-444440000000000000000000000000000000000004-4-44000000000000000000000000000000000000000000000000
χ1004-44-4-44-4-4-44-4-44444000000000000000000000000000000000000-444-4000000000000000000000000000000000000000000000000
χ1014-4-4-444444-4-4-4-444-400000000004i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-444444-4-4-4-444-40000000000−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-4-4-4-444444-4-44400000000004-4-44-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4-4-444444-4-4440000000000-444-44-4-440000000000000000000000000000000000000000000000000000000000000000000000

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