Finite Group Databasebeta

← Group #10691457

Character table — Group #10691457

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12224444223444444666121212124444444444661212121212124444444488881212121212121212121224242424242424244444444444448824242424888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ91111-1-1-1-1-1-1111-1-111111-1-1-1-11-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iii−i−i1-11111-1-1-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−ii−iii−i−i11-1-11-1
χ101111-1-1-1-1-1-1111-1-111111-1-1-1-11-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−iii1-11111-1-1-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i−ii−i−iii-1-111-11
χ111111-1-1-1-1-1-1111-1-111111-1-1-1-11-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiiiii−i−i1-11111-1-1-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiiii−iii−i−i-1-111-11
χ121111-1-1-1-1-1-1111-1-111111-1-1-1-11-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−iii1-11111-1-1-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−ii−i−iii11-1-11-1
χ131111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−iii−i−i1-1-1-1-1-11111iiii−i−i−i−iii−i−i−i−i−i−iiiii−ii−i−iii11-1-1-11
χ141111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−i−i−iii1-1-1-1-1-11111−i−i−i−iiiiiii−i−i−i−i−i−iiiiii−iii−i−i-1-1111-1
χ151111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiiiii−i−i1-1-1-1-1-11111iiii−i−i−i−i−i−iiiiiii−i−i−i−i−ii−i−iii-1-1111-1
χ161111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiii−i−iii1-1-1-1-1-11111−i−i−i−iiiii−i−iiiiiii−i−i−i−ii−iii−i−i11-1-1-11
χ172222222222222-2-2-2-22222222-2-2000000002222-2-2-2-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ182222222222222-2-2-2-22222222-2-2000000002222-2-2-2-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ202222222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ212222222222-1222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ222222222222-1222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2322222222-2-22-2-222222222222-2-222-2-222-2-2-2-2-2-22222000000000000-2-222-2-222-2-200000000000000000000000000000000
χ2422222222-2-22-2-222222222222-2-2-2-222-2-222-2-2-2-22222000000000000-2-2-2-222-2-22200000000000000000000000000000000
χ2522222222-2-22-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-200000000000022000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-22-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-20000000000002200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-222-2-222-2-21111-1-1-1-100000000000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ2822222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-222-2-222-2-21111-1-1-1-100000000000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ2922222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-2-2-222-2-2221111-1-1-1-10000000000001111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ3022222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-2-2-222-2-2221111-1-1-1-10000000000001111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-22-20000000022-2-2-2-2220000000000002-20000000000000000000022-2-2-2-222000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-22-20000000022-2-2-2-2220000000000002-200000000000000000000-2-22222-2-2000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-2-2222-2-2-2-22222-2-222-2-2000000000000-2222-2-2-2-22200000000000000000000000000000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-2-22-2-22222-2-222-2-222-2-2000000000000-22-2-22222-2-200000000000000000000000000000000
χ352222-2-2-2-222-1-2-2-2-222-1-1-11111-2222-2-2-2-222-1-111-1-1110000000000001-1-1-11111-1-133−3−3−3−333000000000000003−3−33000000
χ362222-2-2-2-222-1-2-2-2-222-1-1-11111-2222-2-2-2-222-1-111-1-1110000000000001-1-1-11111-1-1−3−33333−3−300000000000000−333−3000000
χ372222-2-2-2-222-1-2-2-2-222-1-1-11111-22-2-22222-2-2-1-111-1-1110000000000001-111-1-1-1-11133−3−3−3−33300000000000000−333−3000000
χ382222-2-2-2-222-1-2-2-2-222-1-1-11111-22-2-22222-2-2-1-111-1-1110000000000001-111-1-1-1-111−3−33333−3−3000000000000003−3−33000000
χ392222-2-2-2-2-2-222222-2-2222-2-2-2-2-2200000000-2-222-2-2222i2i2i2i−2i−2i−2i−2i0000-220000000000000000−2i−2i2i2i00000000000000000000
χ402222-2-2-2-2-2-222222-2-2222-2-2-2-2-2200000000-2-222-2-222−2i−2i−2i−2i2i2i2i2i0000-2200000000000000002i2i−2i−2i00000000000000000000
χ412222-2-2-2-2-2-2-122-2-222-1-1-111112-22222-2-2-2-211-1-1-1-111000000002i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii0000000000002i−2i−i−iii000000
χ422222-2-2-2-2-2-2-122-2-222-1-1-111112-22222-2-2-2-211-1-1-1-11100000000−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i000000000000−2i2iii−i−i000000
χ432222-2-2-2-2-2-2-122-2-222-1-1-111112-2-2-2-2-2222211-1-1-1-111000000002i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii000000000000−2i2iii−i−i000000
χ442222-2-2-2-2-2-2-122-2-222-1-1-111112-2-2-2-2-2222211-1-1-1-11100000000−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i0000000000002i−2i−i−iii000000
χ4522-2-22i−2i2i−2i002002i−2i2-2-22-22i−2i2i−2i00002i−2i002-200002-22i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000002i−2i002-2000000001+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4622-2-22i−2i2i−2i002002i−2i2-2-22-22i−2i2i−2i00002i−2i002-200002-22i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000002i−2i002-200000000−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4722-2-22i−2i2i−2i002002i−2i2-2-22-22i−2i2i−2i0000−2i2i00-2200002-22i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−2i2i00-22000000001+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4822-2-22i−2i2i−2i002002i−2i2-2-22-22i−2i2i−2i0000−2i2i00-2200002-22i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−2i2i00-2200000000−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4922-2-22i−2i2i−2i00200−2i2i-22-22-22i−2i2i−2i002-2002i−2i000000-22−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000002-2002i−2i0000000000−1−i1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ5022-2-22i−2i2i−2i00200−2i2i-22-22-22i−2i2i−2i002-2002i−2i000000-22−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000002-2002i−2i00000000001+i−1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ5122-2-22i−2i2i−2i00200−2i2i-22-22-22i−2i2i−2i00-2200−2i2i000000-22−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000-2200−2i2i0000000000−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ5222-2-22i−2i2i−2i00200−2i2i-22-22-22i−2i2i−2i00-2200−2i2i000000-22−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000-2200−2i2i00000000001+i−1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ5322-2-2−2i2i−2i2i002002i−2i-22-22-2−2i2i−2i2i002-200−2i2i000000-222i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000002-200−2i2i0000000000−1+i1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ5422-2-2−2i2i−2i2i002002i−2i-22-22-2−2i2i−2i2i002-200−2i2i000000-222i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000002-200−2i2i00000000001−i−1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ5522-2-2−2i2i−2i2i002002i−2i-22-22-2−2i2i−2i2i00-22002i−2i000000-222i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000-22002i−2i0000000000−1+i1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ5622-2-2−2i2i−2i2i002002i−2i-22-22-2−2i2i−2i2i00-22002i−2i000000-222i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000-22002i−2i00000000001−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ5722-2-2−2i2i−2i2i00200−2i2i2-2-22-2−2i2i−2i2i00002i−2i00-2200002-2−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000002i−2i00-22000000001−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ5822-2-2−2i2i−2i2i00200−2i2i2-2-22-2−2i2i−2i2i00002i−2i00-2200002-2−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000002i−2i00-2200000000−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ5922-2-2−2i2i−2i2i00200−2i2i2-2-22-2−2i2i−2i2i0000−2i2i002-200002-2−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−2i2i002-2000000001−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ6022-2-2−2i2i−2i2i00200−2i2i2-2-22-2−2i2i−2i2i0000−2i2i002-200002-2−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−2i2i002-200000000−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ612-2-2222-2-2-2222-200002-2-222-2-200000000002-22-200002i−2i2i−2i2i−2i2i−2i2−22−200000000002−22−22−22−2000000000000000000−i2i2−i2i200
χ622-2-2222-2-2-2222-200002-2-222-2-200000000002-22-200002i−2i2i−2i2i−2i2i−2i−22−220000000000−22−22−22−22000000000000000000i2−i2i2−i200
χ632-2-2222-2-2-2222-200002-2-222-2-200000000002-22-20000−2i2i−2i2i−2i2i−2i2i2−22−200000000002−22−22−22−2000000000000000000i2−i2i2−i200
χ642-2-2222-2-2-2222-200002-2-222-2-200000000002-22-20000−2i2i−2i2i−2i2i−2i2i−22−220000000000−22−22−22−22000000000000000000−i2i2−i2i200
χ652-2-22-2-2222-222-200002-2-2-2-2220000000000-222-200002-22-2-22-22−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000−i2i2i2−i200
χ662-2-22-2-2222-222-200002-2-2-2-2220000000000-222-200002-22-2-22-22i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000i2−i2−i2i200
χ672-2-22-2-2222-222-200002-2-2-2-2220000000000-222-20000-22-222-22-2−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000i2−i2−i2i200
χ682-2-22-2-2222-222-200002-2-2-2-2220000000000-222-20000-22-222-22-2i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000−i2i2i2−i200
χ694444444444-244-4-4-4-4-2-2-2-2-2-2-2-4-400000000-2-2-2-22222000000000000220000000000000000000000000000000000000000
χ7044444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022222222000000000000-2-20000000000000000000000000000000000000000
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χ884-4-4444-4-4-44-24-40000-222-2-2220000000000-22-2200000000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ894-4-4444-4-4-44-24-40000-222-2-2220000000000-22-22000000000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ904-4-44-4-4444-4-24-40000-22222-2-200000000002-2-22000000000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ914-4-44-4-4444-4-24-40000-22222-2-200000000002-2-220000000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ924-4-44-4-444-444-4400004-4-4-4-44400000000004-4-440000000000000000000000000000000000000000000000000000000000
χ934-4-44-4-444-44-2-440000-22222-2-20000000000-222-2000000000000000000000000006−6−66−666−6000000000000000000000000
χ944-4-44-4-444-44-2-440000-22222-2-20000000000-222-200000000000000000000000000−666−66−6−66000000000000000000000000
χ958-88-88i−8i−8i8i00-400000044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i00-400000044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000

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