Finite Group Databasebeta

← Group #164166

Character table — Group #164166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222444444444444444444442244444444444488888888888888884444444888888888888888888888888444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1111iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i111-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1-1-1111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-1-1-1111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1111−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii111-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111111111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11-1-11-1-1
χ10111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111-111-111
χ11111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-111-111
χ12111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-11111-1-11111-1-111111-1-11-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-11-1-1ii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiii1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1111-1-1ii−i−i−i−i−i−iiiii−i−iiiiiii−i−i−i−i-1111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1-1−i−iiiiiii−i−i−i−iii−i−i−i−i−i−iiiii-1111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-11-1-1−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i1-1-1-111
χ1711111111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-111-1-111111111111111111111-11-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-11-1-11-1
χ1811111111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-11111-1-1111-111-11
χ1911111111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-111-1-11111-1-111-1-111-1-1-1-111-1-11-111-11
χ2011111111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-111-1-11111-1-11111-1-11111-1-111-11-1-11-1
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1-11-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii-11-11-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−i1-11-11-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1ii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii1-11-11-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1-11-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i-11-11-11
χ2511111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111111111111111111111-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-11-1-11
χ2611111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111-1-11111-1-111-111-1
χ2711111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-111-1-1-1-11111-111-1
χ2811111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-11111-1-11111-1-11111-1-1-1-11-1-11
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-11−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i-1-1111-1
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-11−i−i−i−iiiiiii−i−iiiii−i−i−i−i−i−iii11-1-1-11
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-11iiii−i−i−i−i−i−iii−i−i−i−iiiiiii−i−i11-1-1-11
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-11iiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iii-1-1111-1
χ332222222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000-2-2-2000000000000000000000000000000
χ3422222222222222222222-2-22222-2-2-2-2-2-2-2-2-2-222222200000000000000000000-2-2-2000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000-222000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-222-2-2-2-200000000000000000000-222000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-222-2-2-2-222-2-222-2-2-2-222-2-222000000000000000000002-22000000000000000000000000000000
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χ422222-2-2-2-222-2-222-2-222-2-2220000-2-22-22-22-200000000−2−222−2−222000000000000000−22−22−22−22−22−22000000000000000000
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χ452222-2-2-2-222-2-2-2-222-2-222220000-2-22-2-22-220000000022−2−222−2−20000000000000002−2−22−222−2−22−22000000000000000000
χ462222-2-2-2-222-2-2-2-222-2-222220000-2-22-2-22-2200000000−2−222−2−222000000000000000−222−22−2−222−22−2000000000000000000
χ472222-2-2-2-222-2-2-2-222-2-222-2-2000022-222-22-200000000i2i2−i2−i2−i2−i2i2i2000000000000000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000000000
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χ502222-2-2-2-2-2-22222-2-2-2-222220000-2-2-222-2-2200000000−2−222−2−2220000000000000002−2−222−22−2−222−2000000000000000000
χ512222-2-2-2-2-2-22222-2-2-2-222-2-20000222-2-222-200000000i2i2−i2−i2−i2−i2i2i2000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000
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χ742-22-2-222-2-22-222i−2i2i−2i−2i2i−2i2i002i−2i−2i2i0000000000−2i2i2-2-2200000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000001−i−1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i1−i−1+i000000
χ752-22-2-222-2-22-222i−2i2i−2i−2i2i−2i2i00−2i2i2i−2i00000000002i−2i-222-2000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000−1−i1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000
χ762-22-2-222-2-22-222i−2i2i−2i−2i2i−2i2i00−2i2i2i−2i00000000002i−2i-222-200000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000001+i−1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000
χ772-22-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i002i−2i−2i2i0000000000−2i2i-222-2000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000−1+i1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000
χ782-22-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i002i−2i−2i2i0000000000−2i2i-222-200000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000001−i−1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000
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χ8244-4-44-44-4000000000000−4i4i4i−4i4i−4i−4i4i000000-4400000000000000000000000000000000000000000000000000000000000
χ8344-4-4-44-440000000000004i−4i0000−4i4i000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000000000
χ8444-4-4-44-440000000000004i−4i0000−4i4i00000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000000000
χ8544-4-4-44-44000000000000−4i4i00004i−4i000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000000000
χ8644-4-4-44-44000000000000−4i4i00004i−4i00000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000000000
χ874-44-44-4-444-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ884-44-44-4-444-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ894-44-44-4-44-444-44i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ904-44-44-4-44-444-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ914-4-44-4-4440000000000000044-4-40000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ924-4-44-4-4440000000000000044-4-4000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ934-4-44-4-44400000000000000-4-44400000000000000000000000022−22−2222−222222−220000000000000000000000000000000000000
χ944-4-44-4-44400000000000000-4-444000000000000000000000000−222222−2222−22−22220000000000000000000000000000000000000
χ958-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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