Finite Group Databasebeta

← Group #10712708

Character table — Group #10712708

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size111122222244444444668888888888888888121212161616161616161616161616162424242424242424484848
order12222236662222446644444444666612121212121244424466121212121212121224444444444
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1
χ311111111111111111111-1-11111111111-1-1-1-1111-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1
χ411111111111111111111-1-1-1-1-1-1111111-1-1-1-1111-111-1-1-1-1-1-1111111-1-1-1-1-1-1-111
χ5111111111111111111-1-11111111111111111-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111-1-111-1-1-1-11111111111-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ7111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111
χ8111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111111-1-1
χ91111111111-1-1-1-111111111ii−i−i-1-1-1-11111111-1-1-1i−i-1-1ii−i−iii−i−i1-111ii−i−i-1i−i
χ101111111111-1-1-1-111111111−i−iii-1-1-1-11111111-1-1-1−ii-1-1−i−iii−i−iii1-111−i−iii-1−ii
χ111111111111-1-1-1-1111111-1-1ii−i−i-1-1-1-111-1-1-1-11-1-11−ii11ii−i−i−i−iii1-1-1-1ii−i−i1−ii
χ121111111111-1-1-1-1111111-1-1−i−iii-1-1-1-111-1-1-1-11-1-11i−i11−i−iiiii−i−i1-1-1-1−i−iii1i−i
χ131111111111-1-1-1-11111-1-111ii−i−i-1-1-1-1111111-111-1i−i-1-1ii−i−iii−i−i-11-1-1−i−iii1−ii
χ141111111111-1-1-1-11111-1-111−i−iii-1-1-1-1111111-111-1−ii-1-1−i−iii−i−iii-11-1-1ii−i−i1i−i
χ151111111111-1-1-1-11111-1-1-1-1ii−i−i-1-1-1-111-1-1-1-1-1111−ii11ii−i−i−i−iii-1111−i−iii-1i−i
χ161111111111-1-1-1-11111-1-1-1-1−i−iii-1-1-1-111-1-1-1-1-1111i−i11−i−iiiii−i−i-1111ii−i−i-1−ii
χ1722222222222-2-22-2-222220000002-22-2-2-200002220000000000000-2-2000000000
χ1822222222222-2-22-2-222-2-20000002-22-2-2-20000-2-2-2000000000000022000000000
χ192222222222-222-2-2-22222000000-22-22-2-200002-2-20000000000000-22000000000
χ202222222222-222-2-2-222-2-2000000-22-22-2-20000-22200000000000002-2000000000
χ21222222-1-1-1-1222222-1-100222222-1-1-1-1-1-1-1-1-1-1000222-1-1-1-1-1-1-1-1-1-100000000000
χ22222222-1-1-1-1222222-1-10022-2-2-2-2-1-1-1-1-1-1-1-1-1-10002-2-2-1-11111111100000000000
χ23222222-1-1-1-1222222-1-100-2-22222-1-1-1-1-1-11111000-2-2-211-1-1-1-1111100000000000
χ24222222-1-1-1-1222222-1-100-2-2-2-2-2-2-1-1-1-1-1-11111000-222111111-1-1-1-100000000000
χ25222222-1-1-1-1-2-2-2-222-1-100222i2i−2i−2i1111-1-1-1-1-1-1000-22i−2i11−i−iii−i−iii00000000000
χ26222222-1-1-1-1-2-2-2-222-1-10022−2i−2i2i2i1111-1-1-1-1-1-1000-2−2i2i11ii−i−iii−i−i00000000000
χ27222222-1-1-1-1-2-2-2-222-1-100-2-22i2i−2i−2i1111-1-111110002−2i2i-1-1−i−iiiii−i−i00000000000
χ28222222-1-1-1-1-2-2-2-222-1-100-2-2−2i−2i2i2i1111-1-1111100022i−2i-1-1ii−i−i−i−iii00000000000
χ292-2-222-22-2-2222-2-22-2-22000000002-2-222-20000000000000000000000002i−2i2i−2i000
χ302-2-222-22-2-2222-2-22-2-22000000002-2-222-2000000000000000000000000−2i2i−2i2i000
χ312-2-222-22-2-222-22-2-22-2200002i−2i2i−2i22-2-2-220000000000002i−2i2i−2i000000000000000
χ322-2-222-22-2-222-22-2-22-220000−2i2i−2i2i22-2-2-22000000000000−2i2i−2i2i000000000000000
χ332-2-222-22-2-22-22-22-22-2200002-2-22-2-222-220000000000002-2-22000000000000000
χ342-2-222-22-2-22-22-22-22-220000-222-2-2-222-22000000000000-222-2000000000000000
χ352-2-222-22-2-22-2-2222-2-2200000000-222-22-20000000000000000000000002-2-22000
χ362-2-222-22-2-22-2-2222-2-2200000000-222-22-2000000000000000000000000-222-2000
χ372-2-222-2-111-12-22-2-221-100002i−2i2i−2i-1-1111-1−i3−i3i3i3000000−i3i3−ii−ii3−33−300000000000
χ382-2-222-2-111-12-22-2-221-100002i−2i2i−2i-1-1111-1i3i3−i3−i3000000i3−i3−ii−ii−33−3300000000000
χ392-2-222-2-111-12-22-2-221-10000−2i2i−2i2i-1-1111-1−i3−i3i3i3000000−i3i3i−ii−i−33−3300000000000
χ402-2-222-2-111-12-22-2-221-10000−2i2i−2i2i-1-1111-1i3i3−i3−i3000000i3−i3i−ii−i3−33−300000000000
χ412-2-222-2-111-1-22-22-221-100002-2-2211-1-11-1−i3−i3i3i3000000i3−i3-111-1−i3i3i3−i300000000000
χ422-2-222-2-111-1-22-22-221-100002-2-2211-1-11-1i3i3−i3−i3000000−i3i3-111-1i3−i3−i3i300000000000
χ432-2-222-2-111-1-22-22-221-10000-222-211-1-11-1−i3−i3i3i3000000i3−i31-1-11i3−i3−i3i300000000000
χ442-2-222-2-111-1-22-22-221-10000-222-211-1-11-1i3i3−i3−i3000000−i3i31-1-11−i3i3i3−i300000000000
χ45444444-2-2-2-24-4-44-4-4-2-200000000-22-22220000000000000000000000000000000
χ46444444-2-2-2-2-444-4-4-4-2-2000000002-22-2220000000000000000000000000000000
χ474444-4-44444000000-4-4440000000000000000-400000000000000000000000000
χ484444-4-44444000000-4-4-4-40000000000000000400000000000000000000000000
χ4944-4-40044-4-4000000004i−4i2-200000000002-22-20000000000000000002i−2i0000000
χ5044-4-40044-4-4000000004i−4i-220000000000-22-22000000000000000000−2i2i0000000
χ5144-4-40044-4-400000000−4i4i2-200000000002-22-2000000000000000000−2i2i0000000
χ5244-4-40044-4-400000000−4i4i-220000000000-22-220000000000000000002i−2i0000000
χ534-4-444-4-222-244-4-44-42-200000000-222-2-220000000000000000000000000000000
χ544-4-444-4-222-2-4-4444-42-2000000002-2-22-220000000000000000000000000000000
χ554-4-44-444-4-440000004-400000000000000000004-4000000000000000000000000
χ564-4-44-444-4-440000004-40000000000000000000-44000000000000000000000000
χ578888-8-8-4-4-4-400000044000000000000000000000000000000000000000000000
χ5888-8-800-4-44400000000004-40000000000-22-22000000000000000000000000000
χ5988-8-800-4-4440000000000-4400000000002-22-2000000000000000000000000000
χ608-88-8008-88-800000000000000000000000000000000000000000000000000000
χ618-88-800-44-440000000000000000000000−2i32i32i3−2i3000000000000000000000000000
χ628-88-800-44-4400000000000000000000002i3−2i3−2i32i3000000000000000000000000000
χ638-8-88-88-444-4000000-44000000000000000000000000000000000000000000000

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