Finite Group Databasebeta

← Group #10692408

Character table — Group #10692408

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222222244444444444888888881212121216161616161616161616161616161616242424242424242424244848
order122234444666244446612121212888812121212888824446612121212121224242424244488888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ511111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ611111111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111-1-1-1-1111-111-11-1-1-1-1-1-1ii−i−i11-11ii−i−i1-1i−i11-1-1ii−i−iii−i−i1-1-11ii−i−ii−i1-1
χ1011111-1-1-1-1111-111-11-1-1-1-1-1-1ii−i−i11-11ii−i−i-11−ii-1-111−i−iiiii−i−i1-1-11−i−iiii−i-11
χ1111111-1-1-1-1111-111-11-1-1-1-1-1-1ii−i−i11-11−i−iii1-1i−i11-1-1ii−i−iii−i−i-111-1−i−iii−ii-11
χ1211111-1-1-1-1111-111-11-1-1-1-1-1-1ii−i−i11-11−i−iii-11−ii-1-111−i−iiiii−i−i-111-1ii−i−i−ii1-1
χ1311111-1-1-1-1111-111-11-1-1-1-1-1-1−i−iii11-11ii−i−i1-1−ii11-1-1−i−iii−i−iii-111-1ii−i−ii−i-11
χ1411111-1-1-1-1111-111-11-1-1-1-1-1-1−i−iii11-11ii−i−i-11i−i-1-111ii−i−i−i−iii-111-1−i−iiii−i1-1
χ1511111-1-1-1-1111-111-11-1-1-1-1-1-1−i−iii11-11−i−iii1-1−ii11-1-1−i−iii−i−iii1-1-11−i−iii−ii1-1
χ1611111-1-1-1-1111-111-11-1-1-1-1-1-1−i−iii11-11−i−iii-11i−i-1-111ii−i−i−i−iii1-1-11ii−i−i−ii-11
χ17222222222222-22-2-2-2-2-2222200002-2-2-22222000000000000000000000000-2-200
χ18222222222222-22-2-2-2-2-2222200002-2-2-2-2-2-2-20000000000000000000000002200
χ192222222-2-22222-2-2-222222-2-20000-2-2-220000000000000000000022-2-200000000
χ202222222-2-22222-2-2-222222-2-20000-2-2-2200000000000000000000-2-22200000000
χ212222222-2-2222-2-222-2-2-222-2-22i−2i2i−2i-222-200000000000000002i−2i2i−2i000000000000
χ222222222-2-2222-2-222-2-2-222-2-2−2i2i−2i2i-222-20000000000000000−2i2i−2i2i000000000000
χ2322222-2-2222222-22-2-222-2-2222-2-22-22-2-200000000000000002-2-22000000000000
χ2422222-2-2222222-22-2-222-2-222-222-2-22-2-20000000000000000-222-2000000000000
χ2522222-2-222222-2-2-222-2-2-2-2220000-2-222000000000000000000002-22-200000000
χ2622222-2-222222-2-2-222-2-2-2-2220000-2-22200000000000000000000-22-2200000000
χ2722222-2-2-2-222222-22-222-2-2-2-200002-22-22i2i−2i−2i000000000000000000000000−2i2i00
χ2822222-2-2-2-222222-22-222-2-2-2-200002-22-2−2i−2i2i2i0000000000000000000000002i−2i00
χ292222-12222-1-1-122222-1-1-1-1-1-12222-1-1-1-100002222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ302222-12222-1-1-122222-1-1-1-1-1-12222-1-1-1-10000-2-2-2-211111111-1-1-1-1000000000000
χ312222-12222-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-2-1-1-1-111111111000000000000
χ322222-12222-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-2221111-1-1-1-11111000000000000
χ332222-122-2-2-1-1-1-2-222-211-1-1112i−2i2i−2i1-1-1100000000−i3i3−i3i33−33−3−ii−ii000000000000
χ342222-122-2-2-1-1-1-2-222-211-1-1112i−2i2i−2i1-1-1100000000i3−i3i3−i3−33−33−ii−ii000000000000
χ352222-122-2-2-1-1-1-2-222-211-1-111−2i2i−2i2i1-1-1100000000−i3i3−i3i3−33−33i−ii−i000000000000
χ362222-122-2-2-1-1-1-2-222-211-1-111−2i2i−2i2i1-1-1100000000i3−i3i3−i33−33−3i−ii−i000000000000
χ372222-1-2-222-1-1-12-22-2-2-1-111-1-12-2-221-11100000000−i3i3i3−i3−i3i3i3−i3-111-1000000000000
χ382222-1-2-222-1-1-12-22-2-2-1-111-1-12-2-221-11100000000i3−i3−i3i3i3−i3−i3i3-111-1000000000000
χ392222-1-2-222-1-1-12-22-2-2-1-111-1-1-222-21-11100000000−i3i3i3−i3i3−i3−i3i31-1-11000000000000
χ402222-1-2-222-1-1-12-22-2-2-1-111-1-1-222-21-11100000000i3−i3−i3i3−i3i3i3−i31-1-11000000000000
χ412222-1-2-2-2-2-1-1-1-222-221111112i2i−2i−2i-1-11-100002-22i−2i-1-111−i−iii−i−iii000000000000
χ422222-1-2-2-2-2-1-1-1-222-221111112i2i−2i−2i-1-11-10000-22−2i2i11-1-1ii−i−i−i−iii000000000000
χ432222-1-2-2-2-2-1-1-1-222-22111111−2i−2i2i2i-1-11-100002-2−2i2i-1-111ii−i−iii−i−i000000000000
χ442222-1-2-2-2-2-1-1-1-222-22111111−2i−2i2i2i-1-11-10000-222i−2i11-1-1−i−iiiii−i−i000000000000
χ454444-24444-2-2-2-44-4-4-422-2-2-2-20000-222200000000000000000000000000000000
χ464444-244-4-4-2-2-24-4-4-44-2-2-2-2220000222-200000000000000000000000000000000
χ474444-2-4-444-2-2-2-4-4-4442222-2-2000022-2-200000000000000000000000000000000
χ484444-2-4-4-4-4-2-2-244-44-4-2-222220000-22-2200000000000000000000000000000000
χ4944-4-44004i−4i4-4-40000000004i−4i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ5044-4-44004i−4i4-4-40000000004i−4i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ5144-4-4400−4i4i4-4-4000000000−4i4i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ5244-4-4400−4i4i4-4-4000000000−4i4i000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ534-44-444i−4i00-44-400000004i−4i00000000002+2i−2−2i2−2i−2+2i0000000000000000000000000000
χ544-44-444i−4i00-44-400000004i−4i0000000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000
χ554-44-44−4i4i00-44-40000000−4i4i00000000002−2i−2+2i2+2i−2−2i0000000000000000000000000000
χ564-44-44−4i4i00-44-40000000−4i4i0000000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000
χ5788-8-8-4008i−8i-444000000000−4i4i0000000000000000000000000000000000000000
χ5888-8-8-400−8i8i-4440000000004i−4i0000000000000000000000000000000000000000
χ598-88-8-48i−8i004-440000000−4i4i000000000000000000000000000000000000000000
χ608-88-8-4−8i8i004-4400000004i−4i000000000000000000000000000000000000000000
χ618-8-8880000-8-88000000000000000000000000000000000000000000000000000
χ628-8-88-4000044-400000−4i34i300000000000000000000000000000000000000000000
χ638-8-88-4000044-4000004i3−4i300000000000000000000000000000000000000000000

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