Finite Group Databasebeta

← Group #10695838

Character table — Group #10695838

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222224444444444444444888888888888881616161616161616161616164848484848484848
order1222223666224444666666121212124444121212121212121212124444121212121212121222448888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-11-1-1-111
χ811111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1111-1-1
χ9222222222222-2-2-2-2222222-2-2-2-20000-2-2000000002-20022-2-2000000000000
χ10222222222222-2-2-2-2222222-2-2-2-20000-2-200000000-2200-2-222000000000000
χ112222222222-2-22-22-2-2-222-2-222-2-200002-200000000000000000000020-20000
χ122222222222-2-22-22-2-2-222-2-222-2-200002-2000000000000000000000-2020000
χ132222222222-2-2-22-22-2-222-2-2-2-2220000-220000000000000000000020-200000
χ142222222222-2-2-22-22-2-222-2-2-2-2220000-2200000000000000000000-20200000
χ15222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ16222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ17222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000
χ18222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000
χ19222222-1-1-1-122-2-2-2-2-1-1-1-1-1-11111000011−i3−i3−i3−i3i3i3i3i32-200-1-111−i3−i3i3i300000000
χ20222222-1-1-1-122-2-2-2-2-1-1-1-1-1-11111000011−i3−i3−i3−i3i3i3i3i3-220011-1-1i3i3−i3−i300000000
χ21222222-1-1-1-122-2-2-2-2-1-1-1-1-1-11111000011i3i3i3i3−i3−i3−i3−i32-200-1-111i3i3−i3−i300000000
χ22222222-1-1-1-122-2-2-2-2-1-1-1-1-1-11111000011i3i3i3i3−i3−i3−i3−i3-220011-1-1−i3−i3i3i300000000
χ232222-2-222222-222-2-222-2-2-2-222220000-2-200000000002i−2i00002i−2i2i−2i00000000
χ242222-2-222222-222-2-222-2-2-2-222220000-2-20000000000−2i2i0000−2i2i−2i2i00000000
χ252222-2-222222-2-2-22222-2-2-2-2-2-2-2-222-2-22222-2-222-2-200000000000000000000
χ262222-2-222222-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-222-2-22200000000000000000000
χ272222-2-22222-222-2-22-2-2-2-22222-2-20000-220000000000000000000000002-200
χ282222-2-22222-222-2-22-2-2-2-22222-2-20000-22000000000000000000000000-2200
χ292222-2-22222-22-222-2-2-2-2-222-2-22200002-2000000000000000000000000002-2
χ302222-2-22222-22-222-2-2-2-2-222-2-22200002-200000000000000000000000000-22
χ312222-2-2-1-1-1-12-222-2-2-1-11111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i3002i−2i3−33−3−ii−ii00000000
χ322222-2-2-1-1-1-12-222-2-2-1-11111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i300−2i2i−33−33i−ii−i00000000
χ332222-2-2-1-1-1-12-222-2-2-1-11111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i3002i−2i−33−33−ii−ii00000000
χ342222-2-2-1-1-1-12-222-2-2-1-11111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i300−2i2i3−33−3i−ii−i00000000
χ352222-2-2-1-1-1-12-2-2-222-1-11111111122-2-2-1-1-1-111-1-11100003−3−333−3−3300000000
χ362222-2-2-1-1-1-12-2-2-222-1-11111111122-2-2-1-1-1-111-1-1110000−333−3−333−300000000
χ372222-2-2-1-1-1-12-2-2-222-1-111111111-2-222-1-111-1-111-1-100003−3−33−333−300000000
χ382222-2-2-1-1-1-12-2-2-222-1-111111111-2-222-1-111-1-111-1-10000−333−33−3−3300000000
χ39444444-2-2-2-2-4-44-44-422-2-222-2-2220000-220000000000000000000000000000
χ40444444-2-2-2-2-4-4-44-4422-2-22222-2-200002-20000000000000000000000000000
χ414444-4-4-2-2-2-2-444-4-442222-2-2-2-22200002-20000000000000000000000000000
χ424444-4-4-2-2-2-2-44-444-42222-2-222-2-20000-220000000000000000000000000000
χ4344-4-44-444-4-4000000004-40000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ4444-4-44-444-4-4000000004-4000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ4544-4-44-4-2-222000000−2i32i3-22−2i32i300002i−2i2i−2i002ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ1100000000000000000000
χ4644-4-44-4-2-222000000−2i32i3-22−2i32i30000−2i2i−2i2i00−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ1100000000000000000000
χ4744-4-44-4-2-2220000002i3−2i3-222i3−2i300002i−2i2i−2i002ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ700000000000000000000
χ4844-4-44-4-2-2220000002i3−2i3-222i3−2i30000−2i2i−2i2i00−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ700000000000000000000
χ4944-4-4-4444-4-400000000-440000002i−2i−2i2i002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ5044-4-4-4444-4-400000000-44000000−2i2i2i−2i00−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ5144-4-4-44-2-222000000−2i32i32-22i3−2i300002i−2i−2i2i002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ1100000000000000000000
χ5244-4-4-44-2-222000000−2i32i32-22i3−2i30000−2i2i2i−2i00−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ1100000000000000000000
χ5344-4-4-44-2-2220000002i3−2i32-2−2i32i300002i−2i−2i2i002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ700000000000000000000
χ5444-4-4-44-2-2220000002i3−2i32-2−2i32i30000−2i2i2i−2i00−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ700000000000000000000
χ558-88-8008-88-800000000000000000000000000000000000000000000000000
χ568-88-800-44-4400000000000043−43000000000000000000000000000000000000
χ578-88-800-44-44000000000000−4343000000000000000000000000000000000000
χ588-8-88008-8-8800000000000000000000000000000000000000000000000000
χ598-8-8800-444-40000000000000043−430000000000000000000000000000000000
χ608-8-8800-444-400000000000000−43430000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.