Finite Group Databasebeta

← Group #10786708

Character table — Group #10786708

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222244444444444446666888888888888888881212121212121616161616161616161616242424242424484848
order122234444666224448888121212128888244466661212121212242424248888884481212121212122424248888448
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-111-111-1-1111-1-11111111111-1-1-11-1-11-1-1-1-1-1-11111-1-1-1
χ31111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-111-111-1-1111-1-11111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-1111
χ511111111111111-1-11-1-1-1-11111111111-1111111-1-111-1-1-1-111-1-1-1-1-11-11-1-1-111-1-11111-1-1-11-1
χ611111111111111-1-11-1-1-1-111111111-11-1-111-1-11-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1-111-1-111-1-11-11
χ711111111111111-1-11-1-1-1-11111-1-1-1-111-1111111-1-111-1-1-1-1-1-11111-11-11-1-1-111-1-1-1-1-1-1111-11
χ811111111111111-1-11-1-1-1-11111-1-1-1-1-11-1-111-1-11-1-1-1-1-1-1-1-1-1-111111-11111-1-1-11111-1-111-11-1
χ9111111111111-1-1111-1-1-1-1111111111-111-1-11111111-1-1-1-111-1-1-1-11-1-1-1111-1-1-1-111-1-1111-1-1
χ10111111111111-1-1111-1-1-1-111111111-1-11-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-111-1-1-111111-1-1-1-111-111
χ11111111111111-1-1111-1-1-1-11111-1-1-1-11-111-1-11111111-1-1-1-1-1-111111-1-1-1111-1-1-1-1-1-111-1-1-111
χ12111111111111-1-1111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1-1-1-1-11111-111-1-1-1111111111-1-11-1-1
χ13111111111111-1-1-1-111111111111111-1-11-1-1111-1-1111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-11
χ14111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-111-111-1-1-1-1-1-1-1-111-1
χ15111111111111-1-1-1-1111111111-1-1-1-11-1-11-1-1111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1111111-1
χ16111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-111-111-1-1111111-1-11
χ17222222-2-222222222-2-2-222-2-22200000-2-202200-22200-2-222000000000-200-20000000000000
χ18222222-2-2222222-2-2-222-2-2-2-22200000-2202200-2-2-20022-2-2000000000-20020000000000000
χ19222222-2-22222-2-222-222-2-2-2-222000002-20-2-200-2220022-2-2000000000200-20000000000000
χ20222222-2-22222-2-2-2-2-2-2-222-2-22200000220-2-200-2-2-200-2-22200000000020020000000000000
χ2122222-222-22220000-2000022-2-22222200-20022-200-2-20000-2-20000000000000002-20000000
χ2222222-222-22220000-2000022-2-22222-200200-2-2-200220000-2-2000000000000000-220000000
χ2322222-222-22220000-2000022-2-2-2-2-2-2200-20022-200-2-2000022000000000000000-220000000
χ2422222-222-22220000-2000022-2-2-2-2-2-2-200200-2-2-200220000220000000000000002-20000000
χ252222-12222-1-1-1222222222-1-1-1-100002222-1-1-1-1-1-1-1-1-1-1-1-1-1000000222-1-1-1-1-1-1-1-1000000000
χ262222-12222-1-1-1222222222-1-1-1-10000-222-2-1-111-1-1-111-1-1-1-1000000-2-2-2-111-11111000000000
χ272222-12222-1-1-122-2-22-2-2-2-2-1-1-1-1000022-22-1-1-1-1-111-1-11111000000-22-2-1111-1-111000000000
χ282222-12222-1-1-122-2-22-2-2-2-2-1-1-1-10000-22-2-2-1-111-1111111110000002-22-1-1-1111-1-1000000000
χ292222-12222-1-1-1-2-2222-2-2-2-2-1-1-1-100002-22211-1-1-1-1-1-1-111110000002-2-21-1-1-11111000000000
χ302222-12222-1-1-1-2-2222-2-2-2-2-1-1-1-10000-2-22-21111-1-1-1111111000000-222111-1-1-1-1-1000000000
χ312222-12222-1-1-1-2-2-2-222222-1-1-1-100002-2-2211-1-1-111-1-1-1-1-1-1000000-2-22111111-1-1000000000
χ322222-12222-1-1-1-2-2-2-222222-1-1-1-10000-2-2-2-21111-11111-1-1-1-100000022-21-1-11-1-111000000000
χ332222-12-2-22-1-1-12222-2-2-22211-1-100000-2-20-1-1−i3i31-1-1−i3i311-1-10000000001−i3i31−i3i3−i3i3000000000
χ342222-12-2-22-1-1-12222-2-2-22211-1-100000-2-20-1-1i3−i31-1-1i3−i311-1-10000000001i3−i31i3−i3i3−i3000000000
χ352222-12-2-22-1-1-122-2-2-222-2-211-1-100000-220-1-1−i3i3111−i3i3-1-1110000000001i3−i3-1−i3i3i3−i3000000000
χ362222-12-2-22-1-1-122-2-2-222-2-211-1-100000-220-1-1i3−i3111i3−i3-1-1110000000001−i3i3-1i3−i3−i3i3000000000
χ372222-12-2-22-1-1-1-2-222-222-2-211-1-1000002-2011−i3i31-1-1−i3i3-1-111000000000-1−i3i31i3−i3i3−i3000000000
χ382222-12-2-22-1-1-1-2-222-222-2-211-1-1000002-2011i3−i31-1-1i3−i3-1-111000000000-1i3−i31−i3i3−i3i3000000000
χ392222-12-2-22-1-1-1-2-2-2-2-2-2-22211-1-10000022011−i3i3111−i3i311-1-1000000000-1i3−i3-1i3−i3−i3i3000000000
χ402222-12-2-22-1-1-1-2-2-2-2-2-2-22211-1-10000022011i3−i3111i3−i311-1-1000000000-1−i3i3-1−i3i3i3−i3000000000
χ412-2-222200-2-2-222-22i−2i0002i−2i002-222−2−200002-20002i−2i00002i−2i2−2−i2−i2i2i200000000000002−2−i2i2000
χ422-2-222200-2-2-222-22i−2i0002i−2i002-2−2−22200002-20002i−2i00002i−2i−22i2i2−i2−i20000000000000−22i2−i2000
χ432-2-222200-2-2-222-2−2i2i000−2i2i002-222−2−200002-2000−2i2i0000−2i2i2−2i2i2−i2−i200000000000002−2i2−i2000
χ442-2-222200-2-2-222-2−2i2i000−2i2i002-2−2−22200002-2000−2i2i0000−2i2i−22−i2−i2i2i20000000000000−22−i2i2000
χ452-2-222200-2-2-22-222i−2i000−2i2i002-222−2−20000-220002i−2i0000−2i2i2−2i2i2−i2−i20000000000000−22−i2i2000
χ462-2-222200-2-2-22-222i−2i000−2i2i002-2−2−2220000-220002i−2i0000−2i2i−22−i2−i2i2i200000000000002−2i2−i2000
χ472-2-222200-2-2-22-22−2i2i0002i−2i002-222−2−20000-22000−2i2i00002i−2i2−2−i2−i2i2i20000000000000−22i2−i2000
χ482-2-222200-2-2-22-22−2i2i0002i−2i002-2−2−2220000-22000−2i2i00002i−2i−22i2i2−i2−i200000000000002−2−i2i2000
χ4944444-4-4-4-4444000040000-4-4-4-400000000000040000000000000000000000000000000000
χ504444-2-444-4-2-2-20000-40000-2-2220000400-400-2-220022000000000000000000000000000000
χ514444-2-444-4-2-2-20000-40000-2-2220000-40040022200-2-2000000000000000000000000000000
χ524444-2-4-4-4-4-2-2-200004000022220000000000−2i32i3-2002i3−2i3000000000000000000000000000000
χ534444-2-4-4-4-4-2-2-2000040000222200000000002i3−2i3-200−2i32i3000000000000000000000000000000
χ5444-4-4404-404-4-40000000004-4000000000000000000000000022−2222−2200000000000000000000
χ5544-4-4404-404-4-40000000004-40000000000000000000000000−2222−222200000000000000000000
χ5644-4-440-4404-4-4000000000-44004-44-40000000000000000000000000000000000000000000
χ5744-4-440-4404-4-4000000000-4400-44-440000000000000000000000000000000000000000000
χ584-44-440000-44-400000−2i22i200000022−22−22220000000000000−2i22i200002i−2i−2i2i00000000000000000000
χ594-44-440000-44-400000−2i22i2000000−222222−220000000000000−2i22i20000−2i2i2i−2i00000000000000000000
χ604-44-440000-44-4000002i2−2i200000022−22−222200000000000002i2−2i20000−2i2i2i−2i00000000000000000000
χ614-44-440000-44-4000002i2−2i2000000−222222−2200000000000002i2−2i200002i−2i−2i2i00000000000000000000
χ624-4-444-4004-4-4400000000000-442222−22−2200000000000000000−2222000000000000000000000000
χ634-4-444-4004-4-4400000000000-44−22−2222220000000000000000022−22000000000000000000000000
χ644-4-44-2400-422-24-44i−4i0004i−4i00-2200000000-22000−2i2i0000−2i2i00000000000000000000000000
χ654-4-44-2400-422-24-4−4i4i000−4i4i00-2200000000-220002i−2i00002i−2i00000000000000000000000000
χ664-4-44-2400-422-2-444i−4i000−4i4i00-22000000002-2000−2i2i00002i−2i00000000000000000000000000
χ674-4-44-2400-422-2-44−4i4i0004i−4i00-22000000002-20002i−2i0000−2i2i00000000000000000000000000
χ6888-8-8-408-80-444000000000-440000000000000000000000000000000000000000000000000
χ6988-8-8-40-880-4440000000004-40000000000000000000000000000000000000000000000000
χ708-88-8-400004-4400000−4i24i2000000000000000000000002i2−2i20000000000000000000000000000
χ718-88-8-400004-44000004i2−4i200000000000000000000000−2i22i20000000000000000000000000000
χ728-8-88-4-800844-4000000000004-400000000000000000000000000000000000000000000000

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