Finite Group Databasebeta

← Group #193451

Character table — Group #193451

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size1111111111111111222222224444444444444444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222444444444444444422222244444444444444444488888888888888888888888888888888888888888888888824444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-1-1
χ611111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-111
χ711111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111
χ811111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111-1-11-1-1
χ9111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1111-1-1
χ10111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-111
χ11111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-111-1-1-111
χ12111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111-1-1111-1-1
χ13111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111
χ14111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-11111-1-1-1
χ15111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1
χ16111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1111
χ1711111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−iii−i−iii−i−i11-11-1-11-1
χ1811111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii−i−iii−i−iii-1-11-111-11
χ1911111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−iii−i−iii−i−i-1-11-111-11
χ2011111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii−i−iii−i−iii11-11-1-11-1
χ2111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i−i−iii−i−iii11-1-11-1-11
χ2211111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iiiii−i−iii−i−i-1-111-111-1
χ2311111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i−i−iii−i−iii-1-111-111-1
χ2411111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iiiii−i−iii−i−i11-1-11-1-11
χ2511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−iii1-111-1-1-11
χ2611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i−i−iiiii−i−i-11-1-1111-1
χ2711111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iiiii−i−i−i−iii-11-1-1111-1
χ2811111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i1-111-1-1-11
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii−i−iiiii−i−i1-11-11-11-1
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−iii−i−i−i−iii-11-11-11-11
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii−i−iiiii−i−i-11-11-11-11
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−iii−i−i−i−iii1-11-11-11-1
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χ762-2-2-2-22222222-2-2-2-22-2-222-2-220000-22000000000000-22-22-22−2i2i2i−2i2i−2i−2i2i00000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ772-2-2-2-22222222-2-2-2-2-222-2-222-200002-2000000000000-22-222-2000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ782-2-2-2-22222222-2-2-2-2-222-2-222-200002-2000000000000-22-222-200000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ792-2-2-2-22222222-2-2-2-2-222-2-222-20000-220000000000002-22-2-22000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ802-2-2-2-22222222-2-2-2-2-222-2-222-20000-220000000000002-22-2-2200000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ812-2-2-2-2222-2-2-2-222222-2-22-222-200002-20000000000002-2-22-222-2-222-2-2200000000000000002-2-222-2-22000000000000000000000000
χ822-2-2-2-2222-2-2-2-222222-2-22-222-200002-20000000000002-2-22-22-222-2-222-20000000000000000-222-2-222-2000000000000000000000000
χ832-2-2-2-2222-2-2-2-222222-2-22-222-20000-22000000000000-222-22-22-2-222-2-220000000000000000-222-2-222-2000000000000000000000000
χ842-2-2-2-2222-2-2-2-222222-2-22-222-20000-22000000000000-222-22-2-222-2-222-200000000000000002-2-222-2-22000000000000000000000000
χ852-2-2-2-2222-2-2-2-22222-222-22-2-2200002-2000000000000-222-2-22000000002-2-222-2-22-222-2-222-200000000000000000000000000000000
χ862-2-2-2-2222-2-2-2-22222-222-22-2-2200002-2000000000000-222-2-2200000000-222-2-222-22-2-222-2-2200000000000000000000000000000000
χ872-2-2-2-2222-2-2-2-22222-222-22-2-220000-220000000000002-2-222-2000000002-2-222-2-222-2-222-2-2200000000000000000000000000000000
χ882-2-2-2-2222-2-2-2-22222-222-22-2-220000-220000000000002-2-222-200000000-222-2-222-2-222-2-222-200000000000000000000000000000000
χ89444-4-4-44-44-44-444-4-4000000000000000000000000000000000000000000000000000000000000000022−2222−2200000000000000000000
χ90444-4-4-44-44-44-444-4-40000000000000000000000000000000000000000000000000000000000000000−2222−222200000000000000000000
χ91444-4-4-44-4-44-44-4-44400000000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ92444-4-4-44-4-44-44-4-4440000000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ9344-4-44-4-444i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i000000000000
χ9444-4-44-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000
χ9544-4-44-4-44−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i000000000000
χ9644-4-44-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000
χ974-444-4-4-444i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000
χ984-444-4-4-444i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000
χ994-444-4-4-44−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000
χ1004-444-4-4-44−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000
χ1014-4-444-44-44-44-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000000022−2222−2200000000
χ1024-4-444-44-44-44-4-4-4440000000000000000000000000000000000000000000000000000000000000000000000000000−2222−222200000000
χ1034-4-444-44-4-44-4444-4-400000000000000000000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ1044-4-444-44-4-44-4444-4-40000000000000000000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000

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