Finite Group Databasebeta

← Group #10691450

Character table — Group #10691450

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order1222444422344444466612121212222244444466121212121212444444446666888812121212121224242424242424244444444444448824242424888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ91111-1-1-1-1-1-1111-1-111111-1-1-1-111-1-11-111-1-1-1-11111-1-1iiii−i−i−i−i11-1-1ii−i−i1-111-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−ii−iii−i−i11-1-11-1
χ101111-1-1-1-1-1-1111-1-111111-1-1-1-111-1-11-111-1-1-1-11111-1-1iiii−i−i−i−i11-1-1−i−iii1-111-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i−ii−i−iii-1-111-11
χ111111-1-1-1-1-1-1111-1-111111-1-1-1-111-1-11-111-1-1-1-11111-1-1−i−i−i−iiiii11-1-1ii−i−i1-111-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiiii−iii−i−i-1-111-11
χ121111-1-1-1-1-1-1111-1-111111-1-1-1-111-1-11-111-1-1-1-11111-1-1−i−i−i−iiiii11-1-1−i−iii1-111-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−ii−i−iii11-1-11-1
χ131111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1111-1-1-111-1-11111-1-1iiii−i−i−i−i-1-111ii−i−i1-1-1-111iiii−i−i−i−iii−i−i−i−i−i−iiiii−ii−i−iii11-1-1-11
χ141111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1111-1-1-111-1-11111-1-1iiii−i−i−i−i-1-111−i−iii1-1-1-111−i−i−i−iiiiiii−i−i−i−i−i−iiiiii−iii−i−i-1-1111-1
χ151111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1111-1-1-111-1-11111-1-1−i−i−i−iiiii-1-111ii−i−i1-1-1-111iiii−i−i−i−i−i−iiiiiii−i−i−i−i−ii−i−iii-1-1111-1
χ161111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1111-1-1-111-1-11111-1-1−i−i−i−iiiii-1-111−i−iii1-1-1-111−i−i−i−iiiii−i−iiiiiii−i−i−i−ii−iii−i−i11-1-1-11
χ172222222222222-2-2-2-222222220000-2-2000022-2-222-2-22222222200000000-2-2000000000000-2-2-2-200000000000000000000
χ182222222222222-2-2-2-222222220000-2-2000022-2-222-2-2-2-2-2-2-2-2-2-200000000-2-2000000000000222200000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ202222222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000-2-21111000000
χ212222222222-1222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000000011112222-1-11111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ222222222222-1222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1000000001111-2-2-2-2-1-111111111111100000000000022-1-1-1-1000000
χ2322222222-2-22-2-22222222222222-2-2-2-2-2-222-2-222-2-2220000000022-2-20000-2-2-2-22200000000000000000000000000000000
χ2422222222-2-22-2-222222222222-2-222-2-222-2-2-2-222-2-22200000000-2-2220000-2-222-2-200000000000000000000000000000000
χ2522222222-2-22-2-2-2-2-2-222222220000220000-2-2-2-2-2-2-2-200000000000000002200000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-22-2-2-2-2-2-222222220000220000-2-2-2-2-2-2-2-20000000000000000220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-1-2-22222-1-1-1-1-1-1-122-2-2-2-2-2-22211-1-111-1-100000000-1-11100001111-1-1−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ2822222222-2-2-1-2-22222-1-1-1-1-1-1-122-2-2-2-2-2-22211-1-111-1-100000000-1-11100001111-1-1i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ2922222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-222-2-222-2-211-1-111-1-10000000011-1-1000011-1-111−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ3022222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-222-2-222-2-211-1-111-1-10000000011-1-1000011-1-111i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-200002-2000022-2-2-2-22200000000000000002-2000000000000000022-2-2-2-222000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-200002-2000022-2-2-2-22200000000000000002-20000000000000000-2-22222-2-2000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-22222-22-2-2-2-22222-2-2-2-20000000022220000-22-2-2-2-200000000000000000000000000000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-2-2222222222-2-2-2-200000000-2-2-2-20000-22222200000000000000000000000000000000
χ352222-2-2-2-222-1-2-2-2-222-1-1-111112222-22-2-2-2-2-1-1-1-1111100000000-1-1-1-100001-1111133−3−3−3−333000000000000003−3−33000000
χ362222-2-2-2-222-1-2-2-2-222-1-1-111112222-22-2-2-2-2-1-1-1-1111100000000-1-1-1-100001-11111−3−33333−3−300000000000000−333−3000000
χ372222-2-2-2-222-1-2-2-2-222-1-1-11111-2-2-2-2-222222-1-1-1-1111100000000111100001-1-1-1-1-133−3−3−3−33300000000000000−333−3000000
χ382222-2-2-2-222-1-2-2-2-222-1-1-11111-2-2-2-2-222222-1-1-1-1111100000000111100001-1-1-1-1-1−3−33333−3−3000000000000003−3−33000000
χ392222-2-2-2-2-2-222222-2-2222-2-2-2-20000-220000-2-2-2-222222i2i2i2i−2i−2i−2i−2i00000000-22000000000000−2i−2i2i2i00000000000000000000
χ402222-2-2-2-2-2-222222-2-2222-2-2-2-20000-220000-2-2-2-22222−2i−2i−2i−2i2i2i2i2i00000000-220000000000002i2i−2i−2i00000000000000000000
χ412222-2-2-2-2-2-2-122-2-222-1-1-1111122-2-22-222-2-211-1-1-1-11100000000-1-1112i2i−2i−2i-11-1-111−i−i−i−iiiii0000000000002i−2i−i−iii000000
χ422222-2-2-2-2-2-2-122-2-222-1-1-1111122-2-22-222-2-211-1-1-1-11100000000-1-111−2i−2i2i2i-11-1-111iiii−i−i−i−i000000000000−2i2iii−i−i000000
χ432222-2-2-2-2-2-2-122-2-222-1-1-11111-2-2222-2-2-22211-1-1-1-1110000000011-1-12i2i−2i−2i-1111-1-1−i−i−i−iiiii000000000000−2i2iii−i−i000000
χ442222-2-2-2-2-2-2-122-2-222-1-1-11111-2-2222-2-2-22211-1-1-1-1110000000011-1-1−2i−2i2i2i-1111-1-1iiii−i−i−i−i0000000000002i−2i−i−iii000000
χ4522-2-22i−2i2i−2i002002i−2i2-22-2-22i−2i2i−2i002-2002i−2i00002-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i002-20000002i−2i00000000001+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4622-2-22i−2i2i−2i002002i−2i2-22-2-22i−2i2i−2i002-2002i−2i00002-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i002-20000002i−2i0000000000−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4722-2-22i−2i2i−2i002002i−2i2-22-2-22i−2i2i−2i00-2200−2i2i00002-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00-22000000−2i2i00000000001+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4822-2-22i−2i2i−2i002002i−2i2-22-2-22i−2i2i−2i00-2200−2i2i00002-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00-22000000−2i2i0000000000−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4922-2-22i−2i2i−2i00200−2i2i-222-2-22i−2i2i−2i2-20000002i−2i00-2200−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i2-200000000002i−2i00000000−1−i1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ5022-2-22i−2i2i−2i00200−2i2i-222-2-22i−2i2i−2i2-20000002i−2i00-2200−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-200000000002i−2i000000001+i−1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ5122-2-22i−2i2i−2i00200−2i2i-222-2-22i−2i2i−2i-22000000−2i2i00-2200−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i-220000000000−2i2i00000000−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ5222-2-22i−2i2i−2i00200−2i2i-222-2-22i−2i2i−2i-22000000−2i2i00-2200−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i-220000000000−2i2i000000001+i−1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ5322-2-2−2i2i−2i2i002002i−2i-222-2-2−2i2i−2i2i2-2000000−2i2i00-22002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i2-20000000000−2i2i00000000−1+i1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ5422-2-2−2i2i−2i2i002002i−2i-222-2-2−2i2i−2i2i2-2000000−2i2i00-22002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-20000000000−2i2i000000001−i−1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ5522-2-2−2i2i−2i2i002002i−2i-222-2-2−2i2i−2i2i-220000002i−2i00-22002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i-2200000000002i−2i00000000−1+i1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ5622-2-2−2i2i−2i2i002002i−2i-222-2-2−2i2i−2i2i-220000002i−2i00-22002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i-2200000000002i−2i000000001−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ5722-2-2−2i2i−2i2i00200−2i2i2-22-2-2−2i2i−2i2i002-200−2i2i00002-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i002-2000000−2i2i00000000001−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ5822-2-2−2i2i−2i2i00200−2i2i2-22-2-2−2i2i−2i2i002-200−2i2i00002-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i002-2000000−2i2i0000000000−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ5922-2-2−2i2i−2i2i00200−2i2i2-22-2-2−2i2i−2i2i00-22002i−2i00002-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00-220000002i−2i00000000001−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ6022-2-2−2i2i−2i2i00200−2i2i2-22-2-2−2i2i−2i2i00-22002i−2i00002-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00-220000002i−2i0000000000−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ612-2-2222-2-22-222-20000-2-2222-2-200000000002-2002-2002i−2i2i−2i2i−2i2i−2i0000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i20000000000000000002−22−200
χ622-2-2222-2-22-222-20000-2-2222-2-200000000002-2002-2002i−2i2i−2i2i−2i2i−2i0000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2000000000000000000−22−2200
χ632-2-2222-2-22-222-20000-2-2222-2-200000000002-2002-200−2i2i−2i2i−2i2i−2i2i0000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2000000000000000000−22−2200
χ642-2-2222-2-22-222-20000-2-2222-2-200000000002-2002-200−2i2i−2i2i−2i2i−2i2i0000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i20000000000000000002−22−200
χ652-2-22-2-222-2222-20000-2-22-2-2220000000000-22002-2002-22-2-22-2200002−2−220000002−22−2−22−22000000000000000000−222−200
χ662-2-22-2-222-2222-20000-2-22-2-2220000000000-22002-2002-22-2-22-220000−222−2000000−22−222−22−20000000000000000002−2−2200
χ672-2-22-2-222-2222-20000-2-22-2-2220000000000-22002-200-22-222-22-200002−2−220000002−22−2−22−220000000000000000002−2−2200
χ682-2-22-2-222-2222-20000-2-22-2-2220000000000-22002-200-22-222-22-20000−222−2000000−22−222−22−2000000000000000000−222−200
χ694444444444-244-4-4-4-4-2-2-2-2-2-2-20000-4-40000-2-222-2-222000000000000000022000000000000000000000000000000000000
χ7044444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-20000440000222222220000000000000000-2-2000000000000000000000000000000000000
χ714444-4-4-4-444-2-4-444-4-4-2-2-2222200004-40000-2-22222-2-20000000000000000-22000000000000000000000000000000000000
χ724444-4-4-4-4-4-4-24444-4-4-2-2-222220000-4400002222-2-2-2-200000000000000002-2000000000000000000000000000000000000
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χ7444-4-44i−4i4i−4i00-2004i−4i4-4-222−2i2i−2i2i00-4400−4i4i0000-2200−2i2i00000000002-20000002i−2i0000000000000000000000000000000000
χ7544-4-44i−4i4i−4i00-200−4i4i-44-222−2i2i−2i2i4-40000004i−4i002-2002i−2i00000000-220000000000−2i2i00000000000000000000000000000000
χ7644-4-44i−4i4i−4i00-200−4i4i-44-222−2i2i−2i2i-44000000−4i4i002-2002i−2i000000002-200000000002i−2i00000000000000000000000000000000
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χ7844-4-4−4i4i−4i4i00-2004i−4i-44-2222i−2i2i−2i-440000004i−4i002-200−2i2i000000002-20000000000−2i2i00000000000000000000000000000000
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χ8044-4-4−4i4i−4i4i00-200−4i4i4-4-2222i−2i2i−2i00-44004i−4i0000-22002i−2i00000000002-2000000−2i2i0000000000000000000000000000000000
χ814-44-44i−4i−4i4i004000000-44-44i−4i−4i4i0000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000000000
χ824-44-44i−4i−4i4i004000000-44-44i−4i−4i4i000000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000000000
χ834-44-4−4i4i4i−4i004000000-44-4−4i4i4i−4i0000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000000000
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χ854-4-4444-4-44-4-24-4000022-2-2-2220000000000-2200-2200000000000000−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ864-4-4444-4-44-4-24-4000022-2-2-2220000000000-2200-22000000000000002i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
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χ894-4-4444-4-4-44-2-44000022-2-2-22200000000002-2002-2000000000000000000000000−666−6−666−6000000000000000000000000
χ904-4-44-4-4444-44-440000-4-44-4-44400000000004-400-4400000000000000000000000000000000000000000000000000000000
χ914-4-44-4-4444-4-2-44000022-222-2-20000000000-22002-2000000000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ924-4-44-4-4444-4-2-44000022-222-2-20000000000-22002-2000000000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ934-4-44-4-444-44-24-4000022-222-2-200000000002-200-220000000000000022−22−2222000000−22−222−22−2000000000000000000000000
χ944-4-44-4-444-44-24-4000022-222-2-200000000002-200-2200000000000000−222222−220000002−22−2−22−22000000000000000000000000
χ958-88-88i−8i−8i8i00-40000004-44−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i00-40000004-444i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000

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