Finite Group Databasebeta

← Group #10707210

Character table — Group #10707210

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222222222444444448888888888888888161616161616161616161616242424242424242448484848
order1222344444466612121212888812121212888824242424242424242424242424668812122424242416161616161616162488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ91111111-1-1-1-1111-1-1-1-111-1-111-1-1i−ii−iii−i−i11-1-1ii−i−i1-111i−i-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ101111111-1-1-1-1111-1-1-1-111-1-111-1-1i−ii−iii−i−i11-1-1ii−i−i1-111i−i-1-1ii−i−i-1-111−i−iii-11−ii
χ111111111-1-1-1-1111-1-1-1-111-1-111-1-1i−ii−iii−i−i11-1-1ii−i−i-11-1-1−ii11−i−iii11-1-1ii−i−i-11−ii
χ121111111-1-1-1-1111-1-1-1-111-1-111-1-1i−ii−iii−i−i11-1-1ii−i−i-11-1-1−ii11−i−iii-1-111−i−iii1-1i−i
χ131111111-1-1-1-1111-1-1-1-111-1-111-1-1−ii−ii−i−iii11-1-1−i−iii1-111−ii-1-1−i−iii11-1-1−i−iii1-1−ii
χ141111111-1-1-1-1111-1-1-1-111-1-111-1-1−ii−ii−i−iii11-1-1−i−iii1-111−ii-1-1−i−iii-1-111ii−i−i-11i−i
χ151111111-1-1-1-1111-1-1-1-111-1-111-1-1−ii−ii−i−iii11-1-1−i−iii-11-1-1i−i11ii−i−i11-1-1−i−iii-11i−i
χ161111111-1-1-1-1111-1-1-1-111-1-111-1-1−ii−ii−i−iii11-1-1−i−iii-11-1-1i−i11ii−i−i-1-111ii−i−i1-1−ii
χ17222222222222222222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000
χ18222222222222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-2-2-22222-2-22i−2i−2i2i2i2i−2i−2i-2-222−2i−2i2i2i000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-2-2-22222-2-2−2i2i2i−2i−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000
χ212222-1222222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ222222-1222222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ232222-1222222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-1111122-1-1-2-2-1-11111000000000000
χ242222-1222222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-11111-2-2112211-1-1-1-1000000000000
χ252222-1222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-1-1-1-11111111100−i3i300−i3i3−i3i3−i3i3000000000000
χ262222-1222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-1-1-1-11111111100i3−i300i3−i3i3−i3i3−i3000000000000
χ272222-1222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-100−i3i300−i3i3i3−i3i3−i3000000000000
χ282222-1222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-100i3−i300i3−i3−i3i3−i3i3000000000000
χ292222-122-2-2-2-2-1-1-1111122-2-2-1-1112i−2i2i−2i−i−iii-1-111−i−iii2-2-1-12i−2i11−i−iii000000000000
χ302222-122-2-2-2-2-1-1-1111122-2-2-1-1112i−2i2i−2i−i−iii-1-111−i−iii-2211−2i2i-1-1ii−i−i000000000000
χ312222-122-2-2-2-2-1-1-1111122-2-2-1-111−2i2i−2i2iii−i−i-1-111ii−i−i2-2-1-1−2i2i11ii−i−i000000000000
χ322222-122-2-2-2-2-1-1-1111122-2-2-1-111−2i2i−2i2iii−i−i-1-111ii−i−i-22112i−2i-1-1−i−iii000000000000
χ332222-122-2-2-2-2-1-1-11111-2-222-1-1112i−2i−2i2i−i−iii11-1-1ii−i−i00−i3i300i3−i33−3−33000000000000
χ342222-122-2-2-2-2-1-1-11111-2-222-1-1112i−2i−2i2i−i−iii11-1-1ii−i−i00i3−i300−i3i3−333−3000000000000
χ352222-122-2-2-2-2-1-1-11111-2-222-1-111−2i2i2i−2iii−i−i11-1-1−i−iii00−i3i300i3−i3−333−3000000000000
χ362222-122-2-2-2-2-1-1-11111-2-222-1-111−2i2i2i−2iii−i−i11-1-1−i−iii00i3−i300−i3i33−3−33000000000000
χ3722-2-222-22i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i2-22i−2i000000002-22i−2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ3822-2-222-22i−2i2i−2i2-2-22i2i−2i−2i2-22i−2i2-22i−2i000000002-22i−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ3922-2-222-22i−2i2i−2i2-2-22i2i−2i−2i-22−2i2i2-22i−2i00000000-22−2i2i00000000000000002-22i−2i00000000
χ4022-2-222-22i−2i2i−2i2-2-22i2i−2i−2i-22−2i2i2-22i−2i00000000-22−2i2i0000000000000000-22−2i2i00000000
χ4122-2-222-2−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i2-2−2i2i000000002-2−2i2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ4222-2-222-2−2i2i−2i2i2-2-2−2i−2i2i2i2-2−2i2i2-2−2i2i000000002-2−2i2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ4322-2-222-2−2i2i−2i2i2-2-2−2i−2i2i2i-222i−2i2-2−2i2i00000000-222i−2i00000000000000002-2−2i2i00000000
χ4422-2-222-2−2i2i−2i2i2-2-2−2i−2i2i2i-222i−2i2-2−2i2i00000000-222i−2i0000000000000000-222i−2i00000000
χ4544444-4-444-4-444444440000-4-4-4-40000000000000000000000000000000000000000
χ4644444-4-4-4-444444-4-4-4-40000-4-4440000000000000000000000000000000000000000
χ474444-2-4-444-4-4-2-2-2-2-2-2-2000022220000−2i32i3−2i32i300000000000000000000000000000000
χ484444-2-4-444-4-4-2-2-2-2-2-2-20000222200002i3−2i32i3−2i300000000000000000000000000000000
χ494444-2-4-4-4-444-2-2-22222000022-2-2000023−23−232300000000000000000000000000000000
χ504444-2-4-4-4-444-2-2-22222000022-2-20000−232323−2300000000000000000000000000000000
χ5144-4-44-444i−4i−4i4i4-4-44i4i−4i−4i0000-44−4i4i0000000000000000000000000000000000000000
χ5244-4-44-44−4i4i4i−4i4-4-4−4i−4i4i4i0000-444i−4i0000000000000000000000000000000000000000
χ5344-4-4-24-44i−4i4i−4i-222−2i−2i2i2i4-44i−4i-22−2i2i00000000-22−2i2i0000000000000000000000000000
χ5444-4-4-24-44i−4i4i−4i-222−2i−2i2i2i-44−4i4i-22−2i2i000000002-22i−2i0000000000000000000000000000
χ5544-4-4-24-4−4i4i−4i4i-2222i2i−2i−2i4-4−4i4i-222i−2i00000000-222i−2i0000000000000000000000000000
χ5644-4-4-24-4−4i4i−4i4i-2222i2i−2i−2i-444i−4i-222i−2i000000002-2−2i2i0000000000000000000000000000
χ5744-4-4-2-444i−4i−4i4i-222−2i−2i2i2i00002-22i−2i0000000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000
χ5844-4-4-2-444i−4i−4i4i-222−2i−2i2i2i00002-22i−2i000000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000
χ5944-4-4-2-44−4i4i4i−4i-2222i2i−2i−2i00002-2−2i2i000000000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000
χ6044-4-4-2-44−4i4i4i−4i-2222i2i−2i−2i00002-2−2i2i0000000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000
χ618-88-88000000-8-880000000000000000000000000000000000000000000000000000
χ628-88-8-400000044-4−4i34i3−4i34i3000000000000000000000000000000000000000000000000
χ638-88-8-400000044-44i3−4i34i3−4i3000000000000000000000000000000000000000000000000
χ648-8-888000000-88-80000000000000000000000000000000000000000000000000000
χ658-8-88-40000004-4443−43−4343000000000000000000000000000000000000000000000000
χ668-8-88-40000004-44−434343−43000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.