Finite Group Databasebeta

← Group #10695835

Character table — Group #10695835

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222224444444444444444888888888888881616161616161616161616164848484848484848
order122222366622444466661212121212124444612121212121212121224668812122424242424444488
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
χ511111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1
χ811111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111
χ9222222222222-2-2-2-22222-2-2-2-2-2-200002-200000000000000000000002-20000
χ10222222222222-2-2-2-22222-2-2-2-2-2-200002-20000000000000000000000-220000
χ112222222222-2-22-22-222-2-222-2-2220000-2-2000000002-22200-2-2000000000000
χ122222222222-2-22-22-222-2-222-2-2220000-2-200000000-22-2-20022000000000000
χ132222222222-2-2-22-2222-2-2-2-222-2-20000-22000000000000000000002-2000000
χ142222222222-2-2-22-2222-2-2-2-222-2-20000-2200000000000000000000-22000000
χ15222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100000000
χ16222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-211111100000000
χ17222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-1111100000000
χ18222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-100000000
χ19222222-1-1-1-1-2-22-22-2-1-111-1-111-1-1000011−i3−i3i3i3−i3−i3i3i32-2-1-10011−i3−i3i3i300000000
χ20222222-1-1-1-1-2-22-22-2-1-111-1-111-1-1000011−i3−i3i3i3−i3−i3i3i3-221100-1-1i3i3−i3−i300000000
χ21222222-1-1-1-1-2-22-22-2-1-111-1-111-1-1000011i3i3−i3−i3i3i3−i3−i32-2-1-10011i3i3−i3−i300000000
χ22222222-1-1-1-1-2-22-22-2-1-111-1-111-1-1000011i3i3−i3−i3i3i3−i3−i3-221100-1-1−i3−i3i3i300000000
χ232222-2-222222-222-2-2-2-2222222-2-20000-2-20000000000000000000000002i−2i00
χ242222-2-222222-222-2-2-2-2222222-2-20000-2-2000000000000000000000000−2i2i00
χ252222-2-222222-2-2-222-2-222-2-2-2-22222-2-2-22-2-2-2-2222200000000000000000000
χ262222-2-222222-2-2-222-2-222-2-2-2-222-2-222-222222-2-2-2-200000000000000000000
χ272222-2-22222-222-2-22-2-2-2-222-2-2-2-2000022000000000000000000000000002-2
χ282222-2-22222-222-2-22-2-2-2-222-2-2-2-200002200000000000000000000000000-22
χ292222-2-22222-22-222-2-2-2-2-2-2-2222200002-20000000000002-2002-22-200000000
χ302222-2-22222-22-222-2-2-2-2-2-2-2222200002-2000000000000-2200-22-2200000000
χ312222-2-2-1-1-1-12-2-2-22211-1-11111-1-122-2-21-11111-1-1-1-100−i3i300−i3i3−i3i3i3−i300000000
χ322222-2-2-1-1-1-12-2-2-22211-1-11111-1-122-2-21-11111-1-1-1-100i3−i300i3−i3i3−i3−i3i300000000
χ332222-2-2-1-1-1-12-2-2-22211-1-11111-1-1-2-2221-1-1-1-1-1111100−i3i300−i3i3i3−i3−i3i300000000
χ342222-2-2-1-1-1-12-2-2-22211-1-11111-1-1-2-2221-1-1-1-1-1111100i3−i300i3−i3−i3i3i3−i300000000
χ352222-2-2-1-1-1-1-22-222-2111111-1-1-1-10000-11−i3−i3i3i3i3i3−i3−i300−i3i3-22i3−i31-11-100000000
χ362222-2-2-1-1-1-1-22-222-2111111-1-1-1-10000-11−i3−i3i3i3i3i3−i3−i300i3−i32-2−i3i3-11-1100000000
χ372222-2-2-1-1-1-1-22-222-2111111-1-1-1-10000-11i3i3−i3−i3−i3−i3i3i300−i3i32-2i3−i3-11-1100000000
χ382222-2-2-1-1-1-1-22-222-2111111-1-1-1-10000-11i3i3−i3−i3−i3−i3i3i300i3−i3-22−i3i31-11-100000000
χ39444444-2-2-2-244-4-4-4-4-2-2-2-22222220000-220000000000000000000000000000
χ40444444-2-2-2-2-4-4-44-44-2-22222-2-22200002-20000000000000000000000000000
χ414444-4-4-2-2-2-24-444-4-422-2-2-2-2-2-2220000220000000000000000000000000000
χ424444-4-4-2-2-2-2-444-4-442222-2-222220000-2-20000000000000000000000000000
χ4344-4-44-444-4-40000004-4000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ4444-4-44-444-4-40000004-400000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ4544-4-44-4-2-222000000-2200−2i32i300−2i32i32i−2i2i−2i002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ4644-4-44-4-2-222000000-2200−2i32i300−2i32i3−2i2i−2i2i00−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ4744-4-44-4-2-222000000-22002i3−2i3002i3−2i32i−2i2i−2i002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000
χ4844-4-44-4-2-222000000-22002i3−2i3002i3−2i3−2i2i−2i2i00−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000
χ4944-4-4-4444-4-4000000-44000000002i−2i−2i2i00−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ5044-4-4-4444-4-4000000-4400000000−2i2i2i−2i002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ5144-4-4-44-2-2220000002-200−2i32i3002i3−2i32i−2i−2i2i00−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000
χ5244-4-4-44-2-2220000002-200−2i32i3002i3−2i3−2i2i2i−2i002ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000
χ5344-4-4-44-2-2220000002-2002i3−2i300−2i32i32i−2i−2i2i00−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ5444-4-4-44-2-2220000002-2002i3−2i300−2i32i3−2i2i2i−2i002ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ558-88-8008-8-8800000000000000000000000000000000000000000000000000
χ568-88-800-444-400000000−4i34i30000000000000000000000000000000000000000
χ578-88-800-444-4000000004i3−4i30000000000000000000000000000000000000000
χ588-8-88008-88-800000000000000000000000000000000000000000000000000
χ598-8-8800-44-4400000000000043−43000000000000000000000000000000000000
χ608-8-8800-44-44000000000000−4343000000000000000000000000000000000000

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