Finite Group Databasebeta

← Group #10801884

Character table — Group #10801884

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11111111222222222222222222224444444444444444444466666666888888888888888888888888888888881212121212121212121212122424242424242424
order1222222234444444444446666666888888881212121212121212121212124444444422224444666666661212121212121212242424242424242422448888888844444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ911111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1011111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1211111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1311111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1411111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1511111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ1611111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
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χ201-1111-1-1-111-1iiii−i−i−i−i1-111-1-11-1-111-1-1ii−i−i1-1iiii−i−i−i−i1-1−i−i−i−iiiii-11-11−ii−ii-1-111-1-111−i−iii−i−iii11-1-1ii−i−i-11-11−i−iii-1-1111-11-1i−ii−i
χ211-1111-1-1-111-1iiii−i−i−i−i1-111-1-11-1-1-1-111−i−iii1-1iiii−i−i−i−i1-1iiii−i−i−i−i1-1-11i−i−ii11-1-1-1-111ii−i−i−i−iii-1-111−i−iii1-11-1−i−iii-1-1111-1-11i−i−ii
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χ261-1111-1-1-111-1−i−i−i−iiiii1-111-1-11-1-111-1-1−i−iii1-1−i−i−i−iiiii1-1iiii−i−i−i−i-11-11i−ii−i-1-111-1-111ii−i−iii−i−i11-1-1−i−iii-11-11ii−i−i-1-1111-11-1−ii−ii
χ271-1111-1-1-111-1−i−i−i−iiiii1-111-1-11-1-111-1-1−i−iii1-1−i−i−i−iiiii1-1−i−i−i−iiiii1-11-1−ii−ii11-1-111-1-1−i−iii−i−iii11-1-1−i−iii1-11-1−i−iii11-1-11-11-1−ii−ii
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χ3822222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ3922222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-10000000022-2-222-2-2-1-1-1-11111-1-1-1-111111111111100000000000000000000
χ4022222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-100000000-2-222-2-2221111-1-1-1-11111-1-1-1-11111111100000000000000000000
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χ762-22-2-222-2222-22-222-22-2-2-2-2-2-2-22220000000022-22-222-22-2-2-200000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ772-22-2-222-22-2-22-2-22-222-222-2-2-2-22222-2-222-2-22-2-22-2-22-222-222000000000000000000000000000000002-2-222-2-2200000000000000000000
χ782-22-2-222-22-2-22-2-22-222-222-2-2-2-2222-222-2-222-2-2-22-2-22-222-22200000000000000000000000000000000-222-2-222-200000000000000000000
χ792-22-2-222-22-2-2-222-22-2-2222-2-2-2-22222-2-22-222-2-2-2-222-22-2-2222000000000000000000000000000000002-2-22-222-200000000000000000000
χ802-22-2-222-22-2-2-222-22-2-2222-2-2-2-2222-222-22-2-22-2-2-222-22-2-222200000000000000000000000000000000-222-22-2-2200000000000000000000
χ812-22-2-222-2-1-2-22-2-22-222-2221111-1-1-12-2-222-2-2211-111-11-1-11-1-10000000000000000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3-111-1-111-100000000000000000000
χ822-22-2-222-2-1-2-22-2-22-222-2221111-1-1-12-2-222-2-2211-111-11-1-11-1-10000000000000000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3-111-1-111-100000000000000000000
χ832-22-2-222-2-1-2-22-2-22-222-2221111-1-1-1-222-2-222-211-111-11-1-11-1-10000000000000000−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i31-1-111-1-1100000000000000000000
χ842-22-2-222-2-1-2-22-2-22-222-2221111-1-1-1-222-2-222-211-111-11-1-11-1-10000000000000000i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i31-1-111-1-1100000000000000000000
χ852-22-2-222-2-1-2-2-222-22-2-22221111-1-1-12-2-22-222-2111-1-11-111-1-1-10000000000000000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3-111-11-1-1100000000000000000000
χ862-22-2-222-2-1-2-2-222-22-2-22221111-1-1-12-2-22-222-2111-1-11-111-1-1-10000000000000000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3-111-11-1-1100000000000000000000
χ872-22-2-222-2-1-2-2-222-22-2-22221111-1-1-1-222-22-2-22111-1-11-111-1-1-10000000000000000−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i31-1-11-111-100000000000000000000
χ882-22-2-222-2-1-2-2-222-22-2-22221111-1-1-1-222-22-2-22111-1-11-111-1-1-10000000000000000i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i31-1-11-111-100000000000000000000
χ8944444444-2-4-444-4-444-4-4-4-4-2-2-2-2-2-2-20000000022-2-222-2-22222000000000000000000000000000000000000000000000000000000000000
χ9044444444-2-4-4-4-444-4-444-4-4-2-2-2-2-2-2-2000000002222-2-222-2-222000000000000000000000000000000000000000000000000000000000000
χ91444-4-4-4-44-24-44i−4i4i−4i4i−4i4i−4i-4422-2-2-22200000000-22−2i2i−2i2i−2i2i−2i2i2-2000000000000000000000000000000000000000000000000000000000000
χ92444-4-4-4-44-24-4−4i4i−4i4i−4i4i−4i4i-4422-2-2-22200000000-222i−2i2i−2i2i−2i2i−2i2-2000000000000000000000000000000000000000000000000000000000000
χ9344-44-44-4-440000000000004-44-4-44-400000000000000000000004i−4i004i−4i0000000000000000000000000000000000000000000000000000
χ9444-44-44-4-440000000000004-44-4-44-40000000000000000000000−4i4i00−4i4i0000000000000000000000000000000000000000000000000000
χ9544-4-44-44-44000000000000-444-4-4-44000000000000000000004i−4i004i−4i000000000000000000000000000000000000000000000000000000
χ9644-4-44-44-44000000000000-444-4-4-4400000000000000000000−4i4i00−4i4i000000000000000000000000000000000000000000000000000000
χ974-4444-4-4-4-2-444i4i−4i−4i−4i−4i4i4i-44-2-222-222000000002-2−2i−2i2i2i2i2i−2i−2i2-2000000000000000000000000000000000000000000000000000000000000
χ984-4444-4-4-4-2-44−4i−4i4i4i4i4i−4i−4i-44-2-222-222000000002-22i2i−2i−2i−2i−2i2i2i2-2000000000000000000000000000000000000000000000000000000000000
χ994-44-4-444-4-2444-44-4-44-44-4-42222-2-2-200000000-2-2-22-222-22-222000000000000000000000000000000000000000000000000000000000000
χ1004-44-4-444-4-244-44-444-44-4-4-42222-2-2-200000000-2-22-22-2-22-2222000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-4-44440000000000004-4-44-4-4400000000000000000000004-400-440000000000000000000000000000000000000000000000000000
χ1024-4-44-4-44440000000000004-4-44-4-440000000000000000000000-44004-40000000000000000000000000000000000000000000000000000
χ1034-4-4-444-444000000000000-44-44-44-4000000000000000000004-400-44000000000000000000000000000000000000000000000000000000
χ1044-4-4-444-444000000000000-44-44-44-400000000000000000000-44004-4000000000000000000000000000000000000000000000000000000
χ10588-88-88-8-8-4000000000000-44-444-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-88-88-8-40000000000004-4-4444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-8-888-4000000000000-444-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-8-888-88-40000000000004-44-44-4400000000000000000000000000000000000000000000000000000000000000000000000000000000

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