Finite Group Databasebeta

← Group #10695840

Character table — Group #10695840

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222224444444444444444888888888888881616161616161616161616164848484848484848
order12222236662244446666121212121212444461212121212121212124488121212122424242424444488
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1
χ811111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-111-1-111
χ9222222222222-2-2-2-22222-2-2-2-2-2-2000020000-20000000000000000002-20000
χ10222222222222-2-2-2-22222-2-2-2-2-2-2000020000-2000000000000000000-220000
χ112222222222-2-22-22-222-2-222-2-2220000-20000-200002-20022-2-2000000000000
χ122222222222-2-22-22-222-2-222-2-2220000-20000-20000-2200-2-222000000000000
χ132222222222-2-2-22-2222-2-2-2-222-2-20000-20000200000000000000002-2000000
χ142222222222-2-2-22-2222-2-2-2-222-2-20000-2000020000000000000000-22000000
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
χ17222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111-1111122-2-2-1-1-1-1111100000000
χ18222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111-11111-2-2221111-1-1-1-100000000
χ19222222-1-1-1-1-2-22-22-2-1-111-1-111-1-100001−i3−i3i3i31−i3−i3i3i32-200-1-111−i3−i3i3i300000000
χ20222222-1-1-1-1-2-22-22-2-1-111-1-111-1-100001−i3−i3i3i31−i3−i3i3i3-220011-1-1i3i3−i3−i300000000
χ21222222-1-1-1-1-2-22-22-2-1-111-1-111-1-100001i3i3−i3−i31i3i3−i3−i32-200-1-111i3i3−i3−i300000000
χ22222222-1-1-1-1-2-22-22-2-1-111-1-111-1-100001i3i3−i3−i31i3i3−i3−i3-220011-1-1−i3−i3i3i300000000
χ232222-2-222222-222-2-2-2-2222222-2-20000-20000-2000000000000000000002i−2i00
χ242222-2-222222-222-2-2-2-2222222-2-20000-20000-200000000000000000000−2i2i00
χ252222-2-222222-2-2-222-2-222-2-2-2-22222-2-2-222222-2-2-2-200000000000000000000
χ262222-2-222222-2-2-222-2-222-2-2-2-222-2-222-2-2-2-2-22222200000000000000000000
χ272222-2-22222-222-2-22-2-2-2-222-2-2-2-2000020000200000000000000000000002-2
χ282222-2-22222-222-2-22-2-2-2-222-2-2-2-200002000020000000000000000000000-22
χ292222-2-22222-22-222-2-2-2-2-2-2-22222000020000-20000002-200002-22-200000000
χ302222-2-22222-22-222-2-2-2-2-2-2-22222000020000-2000000-220000-22-2200000000
χ312222-2-2-1-1-1-12-2-2-22211-1-11111-1-122-2-21-1-1-1-1-111110000−i3i3−i3i3−i3i3i3−i300000000
χ322222-2-2-1-1-1-12-2-2-22211-1-11111-1-122-2-21-1-1-1-1-111110000i3−i3i3−i3i3−i3−i3i300000000
χ332222-2-2-1-1-1-12-2-2-22211-1-11111-1-1-2-22211111-1-1-1-1-10000−i3i3−i3i3i3−i3−i3i300000000
χ342222-2-2-1-1-1-12-2-2-22211-1-11111-1-1-2-22211111-1-1-1-1-10000i3−i3i3−i3−i3i3i3−i300000000
χ352222-2-2-1-1-1-1-22-222-2111111-1-1-1-10000-1−i3−i3i3i31i3i3−i3−i3002-2−i3i3i3−i3-11-1100000000
χ362222-2-2-1-1-1-1-22-222-2111111-1-1-1-10000-1−i3−i3i3i31i3i3−i3−i300-22i3−i3−i3i31-11-100000000
χ372222-2-2-1-1-1-1-22-222-2111111-1-1-1-10000-1i3i3−i3−i31−i3−i3i3i3002-2i3−i3−i3i3-11-1100000000
χ382222-2-2-1-1-1-1-22-222-2111111-1-1-1-10000-1i3i3−i3−i31−i3−i3i3i300-22−i3i3i3−i31-11-100000000
χ39444444-2-2-2-244-4-4-4-4-2-2-2-22222220000-200002000000000000000000000000
χ40444444-2-2-2-2-4-4-44-44-2-22222-2-222000020000-2000000000000000000000000
χ414444-4-4-2-2-2-24-444-4-422-2-2-2-2-2-2220000200002000000000000000000000000
χ424444-4-4-2-2-2-2-444-4-442222-2-222220000-20000-2000000000000000000000000
χ434-44-44-44-44-40000004-4000000002i−2i2i−2i02i−2i2i−2i02i−2i2i−2i00000000000000000000
χ444-44-44-44-44-40000004-400000000−2i2i−2i2i0−2i2i−2i2i0−2i2i−2i2i00000000000000000000
χ454-44-44-4-22-22000000-2200−2i32i300−2i32i32i−2i2i−2i02ζ7−2ζ72ζ11−2ζ1102ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ464-44-44-4-22-22000000-2200−2i32i300−2i32i3−2i2i−2i2i0−2ζ72ζ7−2ζ112ζ110−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ474-44-44-4-22-22000000-22002i3−2i3002i3−2i32i−2i2i−2i02ζ11−2ζ112ζ7−2ζ702ζ11−2ζ112ζ7−2ζ700000000000000000000
χ484-44-44-4-22-22000000-22002i3−2i3002i3−2i3−2i2i−2i2i0−2ζ112ζ11−2ζ72ζ70−2ζ112ζ11−2ζ72ζ700000000000000000000
χ494-44-4-444-44-4000000-44000000002i−2i−2i2i02i−2i2i−2i0−2i2i−2i2i00000000000000000000
χ504-44-4-444-44-4000000-4400000000−2i2i2i−2i0−2i2i−2i2i02i−2i2i−2i00000000000000000000
χ514-44-4-44-22-220000002-200−2i32i3002i3−2i32i−2i−2i2i02ζ11−2ζ112ζ7−2ζ70−2ζ112ζ11−2ζ72ζ700000000000000000000
χ524-44-4-44-22-220000002-200−2i32i3002i3−2i3−2i2i2i−2i0−2ζ112ζ11−2ζ72ζ702ζ11−2ζ112ζ7−2ζ700000000000000000000
χ534-44-4-44-22-220000002-2002i3−2i300−2i32i32i−2i−2i2i02ζ7−2ζ72ζ11−2ζ110−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ544-44-4-44-22-220000002-2002i3−2i300−2i32i3−2i2i2i−2i0−2ζ72ζ7−2ζ112ζ1102ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ5588-8-80088-8-800000000000000000000000000000000000000000000000000
χ5688-8-800-4-44400000000−4i34i30000000000000000000000000000000000000000
χ5788-8-800-4-444000000004i3−4i30000000000000000000000000000000000000000
χ588-8-88008-8-8800000000000000000000000000000000000000000000000000
χ598-8-8800-444-400000000000043−43000000000000000000000000000000000000
χ608-8-8800-444-4000000000000−4343000000000000000000000000000000000000

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