Finite Group Databasebeta

← Group #10692424

Character table — Group #10692424

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881616161616161616161616162424242424242424242424244848
order122234444666244448888121212121212121212126881224242424242424248888242424242424242444448888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ911111-1-1-1-1111-1111-1ii−i−i11-1-111-1-1-1-1-1i−i1iiii−i−i−i−ii−i1-1ii−i−i11-1-11-11-1ii−i−iii−i−i1-1
χ1011111-1-1-1-1111-1111-1ii−i−i11-1-111-1-1-1-1-1i−i1iiii−i−i−i−ii−i1-1ii−i−i11-1-1-11-11−i−iii−i−iii-11
χ1111111-1-1-1-1111-1111-1ii−i−i11-1-111-1-1-1-1-1i−i1iiii−i−i−i−i−ii-11−i−iii-1-1111-11-1ii−i−i−i−iii-11
χ1211111-1-1-1-1111-1111-1ii−i−i11-1-111-1-1-1-1-1i−i1iiii−i−i−i−i−ii-11−i−iii-1-111-11-11−i−iiiii−i−i1-1
χ1311111-1-1-1-1111-1111-1−i−iii11-1-111-1-1-1-1-1−ii1−i−i−i−iiiiii−i-11ii−i−i-1-1111-11-1−i−iiiii−i−i-11
χ1411111-1-1-1-1111-1111-1−i−iii11-1-111-1-1-1-1-1−ii1−i−i−i−iiiiii−i-11ii−i−i-1-111-11-11ii−i−i−i−iii1-1
χ1511111-1-1-1-1111-1111-1−i−iii11-1-111-1-1-1-1-1−ii1−i−i−i−iiiii−ii1-1−i−iii11-1-11-11-1−i−iii−i−iii1-1
χ1611111-1-1-1-1111-1111-1−i−iii11-1-111-1-1-1-1-1−ii1−i−i−i−iiiii−ii1-1−i−iii11-1-1-11-11ii−i−iii−i−i-11
χ17222222222222-22-2-2-222222222-2-222-2-2-2-2-2-222-2-222-2-200000000000000000000000000
χ18222222222222-22-2-2-2-2-2-2-22222-2-222-2-2-222-2-2-222-2-22200000000000000000000000000
χ19222222-2-222222-22-2-20000-2-222-2-2-2-2-2-220020000000000000000000000002i−2i2i−2i000000
χ20222222-2-222222-22-2-20000-2-222-2-2-2-2-2-22002000000000000000000000000−2i2i−2i2i000000
χ21222222-2-22222-2-2-2220000-2-22222-2-222-200-20000000000000000000022-2-20000000000
χ22222222-2-22222-2-2-2220000-2-22222-2-222-200-200000000000000000000-2-2220000000000
χ2322222-222-22222-2-22-20000-2-2-2-22222-2-2200-2000000000000000000002-2-220000000000
χ2422222-222-22222-2-22-20000-2-2-2-22222-2-2200-200000000000000000000-222-20000000000
χ2522222-222-2222-2-22-220000-2-2-2-2-2-22222-20020000000000000000000000002-2-22000000
χ2622222-222-2222-2-22-220000-2-2-2-2-2-22222-2002000000000000000000000000-222-2000000
χ2722222-2-2-2-222222-2-222i2i−2i−2i22-2-2-2-2-2-2222−2i2i-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ2822222-2-2-2-222222-2-22−2i−2i2i2i22-2-2-2-2-2-22222i−2i-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ292222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ302222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ312222-12222-1-1-122222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-2-2-11111111122-2-2-1-1-1-1111100000000000000
χ322222-12222-1-1-122222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-2-2-111111111-2-2221111-1-1-1-100000000000000
χ332222-12222-1-1-1-22-2-2-22222-1-1-1-111-1-1111-2-21-1-111-1-11100003−33−33−33−300000000000000
χ342222-12222-1-1-1-22-2-2-22222-1-1-1-111-1-1111-2-21-1-111-1-1110000−33−33−33−3300000000000000
χ352222-12222-1-1-1-22-2-2-2-2-2-2-2-1-1-1-111-1-111122111-1-111-1-100003−33−3−33−3300000000000000
χ362222-12222-1-1-1-22-2-2-2-2-2-2-2-1-1-1-111-1-111122111-1-111-1-10000−33−333−33−300000000000000
χ372222-1-2-2-2-2-1-1-122-2-222i2i−2i−2i-1-1111111-1-1-1−2i2i1−i−iiiii−i−i0000−i3i3i3−i3−333−300000000000000
χ382222-1-2-2-2-2-1-1-122-2-222i2i−2i−2i-1-1111111-1-1-1−2i2i1−i−iiiii−i−i0000i3−i3−i3i33−3−3300000000000000
χ392222-1-2-2-2-2-1-1-122-2-22−2i−2i2i2i-1-1111111-1-1-12i−2i1ii−i−i−i−iii0000−i3i3i3−i33−3−3300000000000000
χ402222-1-2-2-2-2-1-1-122-2-22−2i−2i2i2i-1-1111111-1-1-12i−2i1ii−i−i−i−iii0000i3−i3−i3i3−333−300000000000000
χ412222-1-2-2-2-2-1-1-1-2222-22i2i−2i−2i-1-111-1-1111112i−2i-1−i−i−i−iiiii2i−2i2-2−i−iii-1-11100000000000000
χ422222-1-2-2-2-2-1-1-1-2222-22i2i−2i−2i-1-111-1-1111112i−2i-1−i−i−i−iiiii−2i2i-22ii−i−i11-1-100000000000000
χ432222-1-2-2-2-2-1-1-1-2222-2−2i−2i2i2i-1-111-1-111111−2i2i-1iiii−i−i−i−i2i−2i-22−i−iii11-1-100000000000000
χ442222-1-2-2-2-2-1-1-1-2222-2−2i−2i2i2i-1-111-1-111111−2i2i-1iiii−i−i−i−i−2i2i2-2ii−i−i-1-11100000000000000
χ454444-24-4-44-2-2-24-44-4-4000022-2-2222222-200-20000000000000000000000000000000000
χ464444-24-4-44-2-2-2-4-4-444000022-2-2-2-222-2-220020000000000000000000000000000000000
χ474444-2-444-4-2-2-24-4-44-400002222-2-2-2-222-20020000000000000000000000000000000000
χ484444-2-444-4-2-2-2-4-44-440000222222-2-2-2-2200-20000000000000000000000000000000000
χ494-44-4404i−4i04-4-40000000000000004i−4i00000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ504-44-4404i−4i04-4-40000000000000004i−4i0000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ514-44-440−4i4i04-4-4000000000000000−4i4i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ524-44-440−4i4i04-4-4000000000000000−4i4i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ534-4-444400-4-44-400000−2i22i2−2i22i2004-40000000000−2i22i200−2i22i20000000000000000000000000000
χ544-4-444400-4-44-4000002i2−2i22i2−2i2004-400000000002i2−2i2002i2−2i20000000000000000000000000000
χ554-4-444-4004-44-40000022−22−222200-44000000000022−2200−22220000000000000000000000000000
χ564-4-444-4004-44-400000−222222−2200-440000000000−22220022−220000000000000000000000000000
χ574-4-44-2400-42-2200000−2i22i2−2i22i200-2223−230023−230000i2−i2i6−i6i2−i2i6−i600000000000000000000000000
χ584-4-44-2400-42-2200000−2i22i2−2i22i200-22−232300−23230000i2−i2−i6i6i2−i2−i6i600000000000000000000000000
χ594-4-44-2400-42-22000002i2−2i22i2−2i200-2223−230023−230000−i2i2−i6i6−i2i2−i6i600000000000000000000000000
χ604-4-44-2400-42-22000002i2−2i22i2−2i200-22−232300−23230000−i2i2i6−i6−i2i2i6−i600000000000000000000000000
χ614-4-44-2-40042-220000022−22−2222002-223−2300−23230000−22−662−26−600000000000000000000000000
χ624-4-44-2-40042-220000022−22−2222002-2−23230023−230000−226−62−2−6600000000000000000000000000
χ634-4-44-2-40042-2200000−222222−22002-223−2300−232300002−26−6−22−6600000000000000000000000000
χ644-4-44-2-40042-2200000−222222−22002-2−23230023−2300002−2−66−226−600000000000000000000000000
χ6588-8-880000-8-88000000000000000000000000000000000000000000000000000000000
χ6688-8-8-4000044-400000000043−430000000000000000000000000000000000000000000000
χ6788-8-8-4000044-4000000000−43430000000000000000000000000000000000000000000000
χ688-88-8-408i−8i0-444000000000000000−4i4i0000000000000000000000000000000000000000
χ698-88-8-40−8i8i0-4440000000000000004i−4i0000000000000000000000000000000000000000

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