Finite Group Databasebeta

← Group #196399

Character table — Group #196399

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222224444444444444444444444444444224444444444888888888888888888888888888888882444444444444444
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
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-11-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-111-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-11-1-11-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-11-111-11−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-11-1-11-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-11-111-11ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-11-1-11ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111-111-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-11-1-11−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111-111-1ii−i−i−i−iii
χ1711111111-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-1-11111-11-11-11-1
χ1811111111-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-11-11-11-11
χ1911111111-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-1111-11-11-11-11
χ2011111111-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11111-1-1-11-11-11-11-1
χ2111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-11-11-1-11-11
χ2211111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-111-11-111-11-1
χ2311111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-1111-1-1-11-111-11-1
χ2411111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-1-1111-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-11-11-1i−i−iii−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11-11-11-11−iii−i−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-11-11-1−iii−i−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-11-11-11i−i−iii−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1-11i−i−ii−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-1-1111-1−iii−ii−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-111-1-1-11−iii−ii−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-1-1111-1i−i−ii−iii−i
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χ342222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-222-2-2-2-222-2-2-2-2000000000000000000000000000000000000000000000000
χ35222222222222-2-2-2-22222222222-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ36222222222222-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-22222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-22222-2-222000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-222222222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
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χ44222-2-22-2-2000022-2-2002i2i−2i−2i0000−2i−2i2i2i-2-222−2i−2i2i2i00000000002i−2i0000-22−i2−i2i2i2−2−222−i2−i2i2i2−2−22222−2−2i2i2−i2−i222−2−2i2i2−i2−i20000000000000000
χ45222-2-22-2-2000022-2-200−2i−2i2i2i00002i2i−2i−2i-2-2222i2i−2i−2i0000000000−2i2i0000-22i2i2−i2−i2−2−222i2i2−i2−i2−2−22222−2−2−i2−i2i2i222−2−2−i2−i2i2i20000000000000000
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χ50222-2-22-2-20000-2-222002i2i−2i−2i00002i2i−2i−2i-2-222−2i−2i2i2i0000000000−2i2i00002-2−2−222−i2−i2i2i222−2−2i2i2−i2−i2i2i2−i2−i222−2−2−i2−i2i2i2−2−2220000000000000000
χ51222-2-22-2-20000-2-222002i2i−2i−2i0000−2i−2i2i2i22-2-22i2i−2i−2i0000000000−2i2i0000-2222−2−2i2i2−i2−i2−2−222−i2−i2i2i2i2i2−i2−i222−2−2−i2−i2i2i2−2−2220000000000000000
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χ632-2-2222-2-222-2-2-22-220000000000−2i2i−2i2i00002i−2i2i−2i2i2i−2i−2i00-220000−2i2i00002−22−22−22−2−22−22−22−22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ642-2-2222-2-222-2-2-22-220000000000−2i2i−2i2i00002i−2i2i−2i2i2i−2i−2i00-220000−2i2i0000−22−22−22−222−22−22−22−2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ652-2-2222-2-2-2-2222-22-200000000002i−2i2i−2i00002i−2i2i−2i−2i−2i2i2i00-220000−2i2i0000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i22−22−2−22−222−22−2−22−220000000000000000
χ662-2-2222-2-2-2-2222-22-200000000002i−2i2i−2i00002i−2i2i−2i−2i−2i2i2i00-220000−2i2i0000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−22−222−22−2−22−222−22−20000000000000000
χ672-2-2222-2-2-2-2222-22-20000000000−2i2i−2i2i0000−2i2i−2i2i2i2i−2i−2i00-2200002i−2i0000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−22−222−22−2−22−222−22−20000000000000000
χ682-2-2222-2-2-2-2222-22-20000000000−2i2i−2i2i0000−2i2i−2i2i2i2i−2i−2i00-2200002i−2i0000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i22−22−2−22−222−22−2−22−220000000000000000
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χ722-2-2222-2-2-2-222-22-220000000000−2i2i−2i2i00002i−2i2i−2i−2i−2i2i2i002-200002i−2i0000−22−222−22−22−22−2−22−22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ732-2-2-2-222200002-2-2222000022-2-22-2-2200002-2-220000-2-2002-200002-20000002i−2i−2i2i00002i−2i−2i2i0000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ742-2-2-2-222200002-2-2222000022-2-22-2-2200002-2-220000-2-2002-200002-2000000−2i2i2i−2i0000−2i2i2i−2i00002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ752-2-2-2-222200002-2-22220000-2-222-222-20000-222-20000-2-2002-20000-220000002i−2i−2i2i00002i−2i−2i2i00002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ762-2-2-2-222200002-2-22220000-2-222-222-20000-222-20000-2-2002-20000-22000000−2i2i2i−2i0000−2i2i2i−2i0000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ772-2-2-2-222200002-2-22-2-2000022-2-2-222-20000-222-200002200-2200002-2002-2-2200002-2-220000-222-20000-222-200000000000000000000
χ782-2-2-2-222200002-2-22-2-2000022-2-2-222-20000-222-200002200-2200002-200-222-20000-222-200002-2-2200002-2-2200000000000000000000
χ792-2-2-2-222200002-2-22-2-20000-2-2222-2-2200002-2-2200002200-220000-22002-2-2200002-2-2200002-2-2200002-2-2200000000000000000000
χ802-2-2-2-222200002-2-22-2-20000-2-2222-2-2200002-2-2200002200-220000-2200-222-20000-222-20000-222-20000-222-200000000000000000000
χ812-2-2-2-22220000-222-222000022-2-2-222-200002-2-220000-2-200-220000-22002i−2i−2i2i0000−2i2i2i−2i0000−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ822-2-2-2-22220000-222-222000022-2-2-222-200002-2-220000-2-200-220000-2200−2i2i2i−2i00002i−2i−2i2i00002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ832-2-2-2-22220000-222-2220000-2-2222-2-220000-222-20000-2-200-2200002-2002i−2i−2i2i0000−2i2i2i−2i00002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ842-2-2-2-22220000-222-2220000-2-2222-2-220000-222-20000-2-200-2200002-200−2i2i2i−2i00002i−2i−2i2i0000−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ852-2-2-2-22220000-222-2-2-2000022-2-22-2-220000-222-2000022002-20000-220000002-2-220000-222-20000-222-200002-2-220000000000000000
χ862-2-2-2-22220000-222-2-2-2000022-2-22-2-220000-222-2000022002-20000-22000000-222-200002-2-2200002-2-220000-222-20000000000000000
χ872-2-2-2-22220000-222-2-2-20000-2-222-222-200002-2-22000022002-200002-20000002-2-220000-222-200002-2-220000-222-20000000000000000
χ882-2-2-2-22220000-222-2-2-20000-2-222-222-200002-2-22000022002-200002-2000000-222-200002-2-220000-222-200002-2-220000000000000000
χ8944-44-4-44-400000000004-44-44i−4i4i−4i0000000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ9044-44-4-44-400000000004-44-4−4i4i−4i4i000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ9144-44-4-44-40000000000-44-444i−4i4i−4i000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ9244-44-4-44-40000000000-44-44−4i4i−4i4i0000000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ9344-4-44-4-444-44-400004i−4i4i−4i−4i4i000000000000000000004i−4i000000000000000000000000000000000000000000000000000000000000
χ9444-4-44-4-444-44-40000−4i4i−4i4i4i−4i00000000000000000000−4i4i000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-44-44-4400004i−4i−4i4i4i−4i000000000000000000004i−4i000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-44-44-440000−4i4i4i−4i−4i4i00000000000000000000−4i4i000000000000000000000000000000000000000000000000000000000000
χ974-444-4-4-44000000004i−4i0000000000004i−4i4i−4i00004-4-44−4i4i000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-44000000004i−4i000000000000−4i4i−4i4i0000-444-4−4i4i000000000000000000000000000000000000000000000000000000000000
χ994-444-4-4-4400000000−4i4i0000000000004i−4i4i−4i0000-444-44i−4i000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-4-4400000000−4i4i000000000000−4i4i−4i4i00004-4-444i−4i000000000000000000000000000000000000000000000000000000000000
χ1014-44-44-44-44-4-4400000000004i−4i−4i4i0000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-44-44-44-4-440000000000−4i4i4i−4i00004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ1034-44-44-44-4-444-400000000004i−4i−4i4i00004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ1044-44-44-44-4-444-40000000000−4i4i4i−4i0000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000

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