Finite Group Databasebeta

← Group #196674

Character table — Group #196674

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222244444444444444444444444444444444222244444444888888888888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-11-11-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-11-11-11-11−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1-11-11-11-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-11-11-11-11ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1-1-111-1-11ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-111-1-111-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1-1-111-1-11−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-111-1-111-1ii−i−i−i−iii
χ1711111111-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11i−ii−ii−ii−i
χ1811111111-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-111-11-1−ii−ii−ii−ii
χ1911111111-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11−ii−ii−ii−ii
χ2011111111-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-111-11-1i−ii−ii−ii−i
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-11-111-1i−ii−i−ii−ii
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-111-11-1-11−ii−iii−ii−i
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-1-11-111-1−ii−iii−ii−i
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-111-11-1-11i−ii−i−ii−ii
χ2511111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-11
χ2611111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1
χ2711111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-111-1
χ2811111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-11
χ2911111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1111-1-11-111-1
χ3011111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-111-11-1-11
χ3111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-111-11-1-11
χ3211111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11-1-11-111-1
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χ34222222222222222222-2-2-2-22222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-222-2-2-2-222000000000000000000000000000000000000000000000000
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χ3722222222-2-2-2-22222-2-22222-2-2-2-22222-2-2-2-222222222-2-222-2-2-2-2-2-222-2-2000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-22222000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-222-2-22222000000000000000000000000000000000000000000000000
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χ632-22-22-22-222-2-2000000−2i2i−2i2i00000000−2i−2i2i2i−2i2i−2i2i2-22-2000000−2i2i00002-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−22−22−22−22−22−22−22−220000000000000000
χ642-22-22-22-222-2-2000000−2i2i−2i2i00000000−2i−2i2i2i−2i2i−2i2i2-22-2000000−2i2i00002-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22−22−22−22−22−22−22−22−20000000000000000
χ652-22-22-22-2-2-2220000002i−2i2i−2i000000002i2i−2i−2i−2i2i−2i2i-22-22000000−2i2i00002-22−22−2−22−222−22−2−22−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
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χ672-22-22-22-2-2-2220000002i−2i2i−2i00000000−2i−2i2i2i2i−2i2i−2i2-22-2000000−2i2i0000-22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i22−22−2−22−22−22−222−22−20000000000000000
χ682-22-22-22-2-2-2220000002i−2i2i−2i00000000−2i−2i2i2i2i−2i2i−2i2-22-2000000−2i2i0000-22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−22−222−22−22−22−2−22−220000000000000000
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χ702-22-22-22-2-2-222000000−2i2i−2i2i000000002i2i−2i−2i−2i2i−2i2i2-22-20000002i−2i0000-22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i22−22−2−22−22−22−222−22−20000000000000000
χ712-22-22-22-2-2-222000000−2i2i−2i2i00000000−2i−2i2i2i2i−2i2i−2i-22-220000002i−2i00002-22−22−2−22−222−22−2−22−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ722-22-22-22-2-2-222000000−2i2i−2i2i00000000−2i−2i2i2i2i−2i2i−2i-22-220000002i−2i00002-2−22−222−22−2−22−222−22−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ732-2-2-2-222200000000222-2-2222-2-2000000002-2-222-2-22-2-2002-2002-2000000002i−2i−2i2i2i−2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ742-2-2-2-222200000000222-2-2222-2-2000000002-2-222-2-22-2-2002-2002-200000000−2i2i2i−2i−2i2i2i−2i000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ752-2-2-2-222200000000222-2-22-2-22200000000-222-2-222-2-2-2002-200-2200002i−2i−2i2i00000000−2i2i2i−2i2i−2i−2i2i00000000−2i2i2i−2i0000000000000000
χ762-2-2-2-222200000000222-2-22-2-22200000000-222-2-222-2-2-2002-200-220000−2i2i2i−2i000000002i−2i−2i2i−2i2i2i−2i000000002i−2i−2i2i0000000000000000
χ772-2-2-2-22220000000022-222-222-2-2000000002-2-22-222-2-2-200-2200-2200002i−2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i000000002i−2i−2i2i0000000000000000
χ782-2-2-2-22220000000022-222-222-2-2000000002-2-22-222-2-2-200-2200-220000−2i2i2i−2i000000002i−2i−2i2i2i−2i−2i2i00000000−2i2i2i−2i0000000000000000
χ792-2-2-2-22220000000022-222-2-2-22200000000-222-22-2-22-2-200-22002-2000000002i−2i−2i2i2i−2i−2i2i000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ802-2-2-2-22220000000022-222-2-2-22200000000-222-22-2-22-2-200-22002-200000000−2i2i2i−2i−2i2i2i−2i00000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ812-2-2-2-222200000000-2-22-2-2222-2-200000000-222-2-222-22200-22002-2000000002-2-22-222-200000000-222-22-2-2200000000000000000000
χ822-2-2-2-222200000000-2-22-2-2222-2-200000000-222-2-222-22200-22002-200000000-222-22-2-22000000002-2-22-222-200000000000000000000
χ832-2-2-2-222200000000-2-22-2-22-2-222000000002-2-222-2-222200-2200-2200002-2-22000000002-2-222-2-22000000002-2-220000000000000000
χ842-2-2-2-222200000000-2-22-2-22-2-222000000002-2-222-2-222200-2200-220000-222-200000000-222-2-222-200000000-222-20000000000000000
χ852-2-2-2-222200000000-2-2-222-222-2-200000000-222-22-2-2222002-200-2200002-2-22000000002-2-22-222-200000000-222-20000000000000000
χ862-2-2-2-222200000000-2-2-222-222-2-200000000-222-22-2-2222002-200-220000-222-200000000-222-22-2-22000000002-2-220000000000000000
χ872-2-2-2-222200000000-2-2-222-2-2-222000000002-2-22-222-222002-2002-2000000002-2-22-222-2000000002-2-22-222-200000000000000000000
χ882-2-2-2-222200000000-2-2-222-2-2-222000000002-2-22-222-222002-2002-200000000-222-22-2-2200000000-222-22-2-2200000000000000000000
χ89444-4-44-4-44-44-44-44-44-40000000000000000000000004-4000000000000000000000000000000000000000000000000000000000000
χ90444-4-44-4-44-44-4-44-44-44000000000000000000000000-44000000000000000000000000000000000000000000000000000000000000
χ91444-4-44-4-4-44-444-44-4-44000000000000000000000000-44000000000000000000000000000000000000000000000000000000000000
χ92444-4-44-4-4-44-44-44-444-40000000000000000000000004-4000000000000000000000000000000000000000000000000000000000000
χ9344-4-44-4-4400004i−4i−4i4i0000004i−4i4i−4i00004-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ9444-4-44-4-4400004i−4i−4i4i000000−4i4i−4i4i0000-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-440000−4i4i4i−4i0000004i−4i4i−4i0000-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-440000−4i4i4i−4i000000−4i4i−4i4i00004-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ974-444-4-4-444-4-4400000000004i−4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-444-4-440000000000−4i4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ994-444-4-4-44-444-400000000004i−4i−4i4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-4-44-444-40000000000−4i4i4i−4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-4444-4-4000000004-4000000004i−4i−4i4i−4i4i4i−4i00000000-44000000000000000000000000000000000000000000000000000000000000
χ1024-4-4444-4-4000000004-400000000−4i4i4i−4i4i−4i−4i4i00000000-44000000000000000000000000000000000000000000000000000000000000
χ1034-4-4444-4-400000000-44000000004i−4i−4i4i4i−4i−4i4i000000004-4000000000000000000000000000000000000000000000000000000000000
χ1044-4-4444-4-400000000-4400000000−4i4i4i−4i−4i4i4i−4i000000004-4000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).