Finite Group Databasebeta

← Group #10836678

Character table — Group #10836678

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888121212121616161616161616161616162424242424242424242424242424
order122222344444466644444446612121212121212122466121212121212121288884488121212122424242444448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ511111111111111111-1-111-1-11111111111-1-1-1-11-1-1-1-11-1-1111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1
χ611111111111111111-1-111-1-11111111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ711111111111111111-1-111-1-11111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111
χ811111111111111111-1-111-1-11111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111
χ91111111-1-11111111-111-1-11111111-1-1-1-11-1-1-1-1-111-1-1-11111-1-11-11-111-1-111-1-111-1-111-1-11-111-1-1
χ101111111-1-11111111-111-1-11111111-1-1-1-11-1-1-1-1-111-1-1-11111-1-1-11-11-1-111-1-111-1-111-1-1111-111-1-1
χ111111111-1-11111111-111-1-11111111-1-1-1-11-1-1-1-1-111-1-1-111-1-1111-11-111-1-111-1-1-1-111-1-111-11-1-111
χ121111111-1-11111111-111-1-11111111-1-1-1-11-1-1-1-1-111-1-1-111-1-111-11-11-1-111-1-11111-1-111-1-1-11-1-111
χ131111111-1-11111111-1-1-1-1-1-1-111111-1-1-1-111111-1-1-111-1-1-111-1-11-1-1111-1-1-1-11111-1-1-1-1111-1-1-111
χ141111111-1-11111111-1-1-1-1-1-1-111111-1-1-1-111111-1-1-111-1-1-111-1-1-111-1-1-11111-1-1-1-11111-1-11-1-1-111
χ151111111-1-11111111-1-1-1-1-1-1-111111-1-1-1-111111-1-1-111-1-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1111-1-1
χ161111111-1-11111111-1-1-1-1-1-1-111111-1-1-1-111111-1-1-111-1-1-1-1-111-111-1-1-11111-1-111-1-1-1-111-1111-1-1
χ17222222222-2-2-2-2222200-2-20022-2-2-2-2-222-20000-20000200000000000000000000000000002i−2i2i−2i
χ18222222222-2-2-2-2222200-2-20022-2-2-2-2-222-20000-2000020000000000000000000000000000−2i2i−2i2i
χ192222222-2-2-2-2-2-2222-200220022-2-2-222-2-2-2000020000-200000000000000000000000000002i−2i−2i2i
χ202222222-2-2-2-2-2-2222-200220022-2-2-222-2-2-2000020000-20000000000000000000000000000−2i2i2i−2i
χ21222222-1222222-1-1-12222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-12222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-21111111100000000000000
χ23222222-1222222-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-1-1-2-211-11111-111000022-2-2-1-1-1-1111100000000000000
χ24222222-1222222-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-1-1-2-211-11111-1110000-2-2221111-1-1-1-100000000000000
χ25222222-1-2-22222-1-1-1-222-2-222-1-1-1-1-11111-1-2-2111-1-1111-1-100002-22-2-1-111-1-11100000000000000
χ26222222-1-2-22222-1-1-1-222-2-222-1-1-1-1-11111-1-2-2111-1-1111-1-10000-22-2211-1-111-1-100000000000000
χ27222222-1-2-22222-1-1-1-2-2-2-2-2-2-2-1-1-1-1-11111-122-1-1111-1-111100002-2-22-1-11111-1-100000000000000
χ28222222-1-2-22222-1-1-1-2-2-2-2-2-2-2-1-1-1-1-11111-122-1-1111-1-11110000-222-211-1-1-1-11100000000000000
χ292222-2-222222-2-2222-2222-2-2-2-2-22-2-2-2-22222-2222-2-2-2-2-222000000000000000000000000000000
χ302222-2-222222-2-2222-2-2-22-222-2-22-2-2-2-2222-22-2-222222-2-2-2000000000000000000000000000000
χ312222-2-2222-2-222222-200-2200-2-2-2222222-20000-20000-200222200000000000000000000-2-20000
χ322222-2-2222-2-222222-200-2200-2-2-2222222-20000-20000-200-2-2-2-200000000000000000000220000
χ332222-2-22-2-222-2-2222222-22-2-2-2-22-2-222-2-22-22-2-2-2-2-222222000000000000000000000000000000
χ342222-2-22-2-222-2-22222-2-2-2222-2-22-2-222-2-222-222-222-2-22-2-2000000000000000000000000000000
χ352222-2-22-2-2-2-2222222002-200-2-2-222-2-2-2-2-200002000020022-2-200000000000000000000-220000
χ362222-2-22-2-2-2-2222222002-200-2-2-222-2-2-2-2-2000020000200-2-222000000000000000000002-20000
χ372222-2-2-12222-2-2-1-1-1-2222-2-2-211-11111-1-1-12-2-1-1-111111-1-100000000−i3i3−i3i3−i3i3−i3i300000000000000
χ382222-2-2-12222-2-2-1-1-1-2222-2-2-211-11111-1-1-12-2-1-1-111111-1-100000000i3−i3i3−i3i3−i3i3−i300000000000000
χ392222-2-2-12222-2-2-1-1-1-2-2-22-22211-11111-1-1-1-2211-1-1-1-1-111100000000−i3i3−i3i3i3−i3i3−i300000000000000
χ402222-2-2-12222-2-2-1-1-1-2-2-22-22211-11111-1-1-1-2211-1-1-1-1-111100000000i3−i3i3−i3−i3i3−i3i300000000000000
χ412222-2-2-1-2-222-2-2-1-1-1222-22-2-211-111-1-111-1-2211111-1-1-1-1-100000000−i3i3i3−i3−i3i3i3−i300000000000000
χ422222-2-2-1-2-222-2-2-1-1-1222-22-2-211-111-1-111-1-2211111-1-1-1-1-100000000i3−i3−i3i3i3−i3−i3i300000000000000
χ432222-2-2-1-2-222-2-2-1-1-12-2-2-222211-111-1-111-12-2-1-11-1-111-11100000000−i3i3i3−i3i3−i3−i3i300000000000000
χ442222-2-2-1-2-222-2-2-1-1-12-2-2-222211-111-1-111-12-2-1-11-1-111-11100000000i3−i3−i3i3−i3i3i3−i300000000000000
χ452-22-22-2200-222-22-2-202i−2i002i−2i2-2-22-200002000002i−2i0002i−2i0000000000000000002i−2i002-2000000
χ462-22-22-2200-222-22-2-202i−2i002i−2i2-2-22-200002000002i−2i0002i−2i000000000000000000−2i2i00-22000000
χ472-22-22-2200-222-22-2-20−2i2i00−2i2i2-2-22-20000200000−2i2i000−2i2i0000000000000000002i−2i00-22000000
χ482-22-22-2200-222-22-2-20−2i2i00−2i2i2-2-22-20000200000−2i2i000−2i2i000000000000000000−2i2i002-2000000
χ492-22-2-22200-22-222-2-202i−2i00−2i2i-22-2-220000200000−2i2i0002i−2i00000000000000002-2002i−2i00000000
χ502-22-2-22200-22-222-2-202i−2i00−2i2i-22-2-220000200000−2i2i0002i−2i0000000000000000-2200−2i2i00000000
χ512-22-2-22200-22-222-2-20−2i2i002i−2i-22-2-2200002000002i−2i000−2i2i00000000000000002-200−2i2i00000000
χ522-22-2-22200-22-222-2-20−2i2i002i−2i-22-2-2200002000002i−2i000−2i2i0000000000000000-22002i−2i00000000
χ53444444-244-4-4-4-4-2-2-2400-4-400-2-222222-2-22000020000-200000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2-4004400-2-2222-2-22220000-20000200000000000000000000000000000000
χ554444-4-4-244-4-444-2-2-2-400-4400222-2-2-2-2-2-22000020000200000000000000000000000000000000
χ564444-4-4-2-4-4-4-444-2-2-24004-400222-2-2222220000-20000-200000000000000000000000000000000
χ5744-4-40044-40000-4-44000000000000004-40000000000000−2i22i2−2i22i200000000000000000000000000
χ5844-4-40044-40000-4-44000000000000004-400000000000002i2−2i22i2−2i200000000000000000000000000
χ5944-4-4004-440000-4-4400000000000000-440000000000000−2i22i22i2−2i200000000000000000000000000
χ6044-4-4004-440000-4-4400000000000000-4400000000000002i2−2i2−2i22i200000000000000000000000000
χ614-44-44-44004-4-444-4-400000004-44-440000-4000000000000000000000000000000000000000000
χ624-44-44-4-2004-4-44-2220000000-22-22-20000200−2i32i3000−2i32i3000000000000000000000000000000000
χ634-44-44-4-2004-4-44-2220000000-22-22-200002002i3−2i30002i3−2i3000000000000000000000000000000000
χ644-44-44-4-200-444-4-22204i−4i004i−4i-222-220000-200000−2i2i000−2i2i000000000000000000000000000000
χ654-44-44-4-200-444-4-2220−4i4i00−4i4i-222-220000-2000002i−2i0002i−2i000000000000000000000000000000
χ664-44-4-444004-44-44-4-40000000-4444-40000-4000000000000000000000000000000000000000000
χ674-44-4-44-2004-44-4-22200000002-2-2-220000200−2i32i30002i3−2i3000000000000000000000000000000000
χ684-44-4-44-2004-44-4-22200000002-2-2-2200002002i3−2i3000−2i32i3000000000000000000000000000000000
χ694-44-4-44-200-44-44-22204i−4i00−4i4i2-222-20000-2000002i−2i000−2i2i000000000000000000000000000000
χ704-44-4-44-200-44-44-2220−4i4i004i−4i2-222-20000-200000−2i2i0002i−2i000000000000000000000000000000
χ7188-8-800-48-8000044-400000000000000-440000000000000000000000000000000000000000000
χ7288-8-800-4-88000044-4000000000000004-40000000000000000000000000000000000000000000
χ738-8-88008000000-88-800000000000000000000000000000000000000000000000000000000000
χ748-8-8800-40000004-44000000000000−4i34i3000000000000000000000000000000000000000000000
χ758-8-8800-40000004-440000000000004i3−4i3000000000000000000000000000000000000000000000

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