Finite Group Databasebeta

← Group #10827768

Character table — Group #10827768

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222222222244444444444488888888888888888888888121212121616161616161616242424242424242424244848
order1222222223666224444666666224444466666612121212121212121212444444121212121212244444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-11-1-11111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1
χ41111111111111111111111111-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111-1-111111111-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ611111111111111111-1-111111111-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ711111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111
χ811111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-111-1-1
χ91111111111111-1-1-1-1111111111-111-1-1-1-1-111-1-1-1-1111111-1-111111-1-1-111-1-1-1-111-1-1-1-1111-1
χ101111111111111-1-1-1-1111111111-111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11-1-1-111-1-111-1-11111-1-1-11
χ111111111111111-1-1-1-111111111-111-11-1-1-1-1-1-111-1-11111-1-1111111-11-1-1-1-111-1-1-1-111-1-111-11
χ121111111111111-1-1-1-111111111-111-11-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-11-1-1-1-1111111-1-111-1-11-1
χ131111111111111-1-1-1-1-1-11111111-1-11-111-1-111-1-1-1-1-1-1-1-111-1-11111-1111-1-1111111-1-1-1-1-1-1-11
χ141111111111111-1-1-1-1-1-11111111-1-11-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-111-1-1-1-11111111-1
χ151111111111111-1-1-1-1-1-1111111-11-1-1111-1-1-1-111-1-1-1-1-1-1-1-11111111-11111-1-111-1-111-1-1-1-11-1
χ161111111111111-1-1-1-1-1-1111111-11-1-1111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1-1-111-1-11111-11
χ17222222222-1-1-1-1222222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1000000000000
χ18222222222-1-1-1-1222222-1-1-1-1-1-1-2-22-2-222-1-11111-1-1-1-1-1-111110000-2-2-1-11111000000000000
χ19222222222-1-1-1-12222-2-2-1-1-1-1-1-122-222-2-2-1-1-1-1-1-1-1-11111-1-1-1-10000-2-2111111000000000000
χ20222222222-1-1-1-12222-2-2-1-1-1-1-1-1-2-2-2-2-2-2-2-1-11111-1-11111111100002211-1-1-1-1000000000000
χ21222222222-1-1-1-1-2-2-2-222-1-1-1-1-1-12-222-2-2-211-1-11111-1-1-1-1-1-11100002-211-1-111000000000000
χ22222222222-1-1-1-1-2-2-2-222-1-1-1-1-1-1-222-22-2-21111-1-111-1-1-1-111-1-10000-221111-1-1000000000000
χ23222222222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-12-2-22-22211-1-111111111-1-1110000-22-1-111-1-1000000000000
χ24222222222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-22-2-22221111-1-111111111-1-100002-2-1-1-1-111000000000000
χ252222-22-2-2-222220000002-2-22-2-20200-20000002200000000-2-22i2i−2i−2i0000000000002i−2i000000
χ262222-22-2-2-222220000002-2-22-2-20200-20000002200000000-2-2−2i−2i2i2i000000000000−2i2i000000
χ272222-22-2-2-222220000002-2-22-2-20-2002000000-2-200000000222i2i−2i−2i000000000000−2i2i000000
χ282222-22-2-2-222220000002-2-22-2-20-2002000000-2-20000000022−2i−2i2i2i0000000000002i−2i000000
χ29222-22-22-2-22222000000-22-2-22-2200-2000002200000000-2-2002i−2i2i−2i00000000002i−2i00000000
χ30222-22-22-2-22222000000-22-2-22-2200-2000002200000000-2-200−2i2i−2i2i0000000000−2i2i00000000
χ31222-22-22-2-22222000000-22-2-22-2-200200000-2-20000000022002i−2i2i−2i0000000000−2i2i00000000
χ32222-22-22-2-22222000000-22-2-22-2-200200000-2-2000000002200−2i2i−2i2i00000000002i−2i00000000
χ33222-2-2-2-222222222-2-200-2-22-2-220000000220000-2-2000000002-2-22000000000000002-20000
χ34222-2-2-2-222222222-2-200-2-22-2-220000000220000-2-200000000-222-200000000000000-220000
χ35222-2-2-2-2222222-2-22200-2-22-2-220000000-2-2000022000000002-2-2200000000000000-220000
χ36222-2-2-2-2222222-2-22200-2-22-2-220000000-2-200002200000000-222-2000000000000002-20000
χ3722-222-2-2-222-2-222-22-222-2-2-222200-2002-22-200002-222-2-200000000002-20000000000000000
χ3822-222-2-2-222-2-222-22-2-2-2-2-2-222200200-222-200002-2-2-2220000000000-220000000000000000
χ3922-222-2-2-222-2-22-22-2222-2-2-222200-200-22-220000-2222-2-20000000000-220000000000000000
χ4022-222-2-2-222-2-22-22-22-2-2-2-2-2222002002-2-220000-22-2-22200000000002-20000000000000000
χ4122-222-2-2-22-111-12-22-222111-1-1-100-2002-2-11−i3i3−i3i3-11-1-111−i3i3−i3i3000000-11−i3i3−i3i3000000000000
χ4222-222-2-2-22-111-12-22-222111-1-1-100-2002-2-11i3−i3i3−i3-11-1-111i3−i3i3−i3000000-11i3−i3i3−i3000000000000
χ4322-222-2-2-22-111-12-22-2-2-2111-1-1-100200-22-11−i3i3−i3i3-1111-1-1−i3i3−i3i30000001-1i3−i3i3−i3000000000000
χ4422-222-2-2-22-111-12-22-2-2-2111-1-1-100200-22-11i3−i3i3−i3-1111-1-1i3−i3i3−i30000001-1−i3i3−i3i3000000000000
χ4522-222-2-2-22-111-1-22-2222111-1-1-100-200-221-1−i3i3i3−i31-1-1-111−i3i3i3−i30000001-1−i3i3i3−i3000000000000
χ4622-222-2-2-22-111-1-22-2222111-1-1-100-200-221-1i3−i3−i3i31-1-1-111i3−i3−i3i30000001-1i3−i3−i3i3000000000000
χ4722-222-2-2-22-111-1-22-22-2-2111-1-1-1002002-21-1−i3i3i3−i31-111-1-1−i3i3i3−i3000000-11i3−i3−i3i3000000000000
χ4822-222-2-2-22-111-1-22-22-2-2111-1-1-1002002-21-1i3−i3−i3i31-111-1-1i3−i3−i3i3000000-11−i3i3i3−i3000000000000
χ4922-2-2-222-222-2-222-2-220022-2-2-2200000002-20000-22000000000000000000002-20000002-200
χ5022-2-2-222-222-2-222-2-220022-2-2-2200000002-20000-2200000000000000000000-22000000-2200
χ5122-2-2-222-222-2-22-222-20022-2-2-220000000-2200002-2000000000000000000002-2000000-2200
χ5222-2-2-222-222-2-22-222-20022-2-2-220000000-2200002-200000000000000000000-220000002-200
χ534444-44-4-4-4-2-2-2-2000000-222-2220400-4000000-2-20000000022000000000000000000000000
χ544444-44-4-4-4-2-2-2-2000000-222-2220-40040000002200000000-2-2000000000000000000000000
χ55444-44-44-4-4-2-2-2-20000002-222-22400-400000-2-2000000002200000000000000000000000000
χ56444-44-44-4-4-2-2-2-20000002-222-22-4004000002200000000-2-200000000000000000000000000
χ57444-4-4-4-444-2-2-2-244-4-40022-222-20000000-2-200002200000000000000000000000000000000
χ58444-4-4-4-444-2-2-2-2-4-4440022-222-20000000220000-2-200000000000000000000000000000000
χ5944-44-4-444-44-4-44000000-4444-4-400000000000000000000000000000000000000000000000
χ6044-44-4-444-4-222-20000002-2-2-22200000000000−2i32i3000000002i3−2i3000000000000000000000000
χ6144-44-4-444-4-222-20000002-2-2-222000000000002i3−2i300000000−2i32i3000000000000000000000000
χ6244-4-444-44-44-4-440000004-44-44-400000000000000000000000000000000000000000000000
χ6344-4-444-44-4-222-2000000-22-22-22000000000−2i32i3000000002i3−2i300000000000000000000000000
χ6444-4-444-44-4-222-2000000-22-22-220000000002i3−2i300000000−2i32i300000000000000000000000000
χ6544-4-4-444-44-222-24-4-4400-2-2222-20000000-2200002-200000000000000000000000000000000
χ6644-4-4-444-44-222-2-444-400-2-2222-200000002-20000-2200000000000000000000000000000000
χ678-80000000800-800004i−4i0000000000000000000004i−4i000000000000000000000000000000
χ688-80000000800-80000−4i4i000000000000000000000−4i4i000000000000000000000000000000
χ698-80000000-4−4i34i3400004i−4i000000000000000000000−2i2i23−230000000000000000000000000000
χ708-80000000-4−4i34i340000−4i4i0000000000000000000002i−2i−23230000000000000000000000000000
χ718-80000000-44i3−4i3400004i−4i000000000000000000000−2i2i−23230000000000000000000000000000
χ728-80000000-44i3−4i340000−4i4i0000000000000000000002i−2i23−230000000000000000000000000000

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