Finite Group Databasebeta

← Group #10697412

Character table — Group #10697412

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222224444444444444444888888888888881616161616161616161616164848484848484848
order12223446662444446612121212121212124444121212121212121212124488121212122424242424448888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-1-1-111
χ611111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1111-1-1
χ711111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ811111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ922222222222-2-22-2-222-2-22222-2-20000-2-20000000000000000000000002-200
χ1022222222222-2-22-2-222-2-22222-2-20000-2-2000000000000000000000000-2200
χ112222222222-22-2-2-22-2-2-2-222-2-2-2-2000022000000002-20022-2-2000000000000
χ122222222222-22-2-2-22-2-2-2-222-2-2-2-200002200000000-2200-2-222000000000000
χ132222222222-2-22-22-2-2-22222-2-2220000-2-200000000000000000000020-20000
χ142222222222-2-22-22-2-2-22222-2-2220000-2-2000000000000000000000-2020000
χ1522222-2-222222-2-22-222-2-2-2-2-2-2220000-2200000000002-2000022-2-200000000
χ1622222-2-222222-2-22-222-2-2-2-2-2-2220000-220000000000-220000-2-22200000000
χ1722222-2-22222-22-2-222222-2-2-2-2-2-200002-2000000000000000000000000002-2
χ1822222-2-22222-22-2-222222-2-2-2-2-2-200002-200000000000000000000000000-22
χ1922222-2-2222-2222-2-2-2-222-2-222-2-22i2i−2i−2i-222i2i2i2i−2i−2i−2i−2i00000000000000000000
χ2022222-2-2222-2222-2-2-2-222-2-222-2-2−2i−2i2i2i-22−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ2122222-2-2222-2-2-2222-2-2-2-2-2-2222200002-20000000000000000000020-200000
χ2222222-2-2222-2-2-2222-2-2-2-2-2-2222200002-200000000000000000000-20200000
χ232222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ242222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ252222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000
χ262222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000
χ272222-122-1-1-1-22-2-2-221111-1-111110000-1-133−3−333−3−32-200-1-1113−33−300000000
χ282222-122-1-1-1-22-2-2-221111-1-111110000-1-133−3−333−3−3-220011-1-1−33−3300000000
χ292222-122-1-1-1-22-2-2-221111-1-111110000-1-1−3−333−3−3332-200-1-111−33−3300000000
χ302222-122-1-1-1-22-2-2-221111-1-111110000-1-1−3−333−3−333-220011-1-13−33−300000000
χ312222-1-2-2-1-1-122-2-22-2-1-1111111-1-100001-1−i3−i3i3i3i3i3−i3−i3002-2−i3i3−i3i3-1-11100000000
χ322222-1-2-2-1-1-122-2-22-2-1-1111111-1-100001-1−i3−i3i3i3i3i3−i3−i300-22i3−i3i3−i311-1-100000000
χ332222-1-2-2-1-1-122-2-22-2-1-1111111-1-100001-1i3i3−i3−i3−i3−i3i3i3002-2i3−i3i3−i3-1-11100000000
χ342222-1-2-2-1-1-122-2-22-2-1-1111111-1-100001-1i3i3−i3−i3−i3−i3i3i300-22−i3i3−i3i311-1-100000000
χ352222-1-2-2-1-1-1-2222-2-211-1-111-1-1112i2i−2i−2i1-1−i−i−i−iiiii0000−i3i3i3−i33−3−3300000000
χ362222-1-2-2-1-1-1-2222-2-211-1-111-1-1112i2i−2i−2i1-1−i−i−i−iiiii0000i3−i3−i3i3−333−300000000
χ372222-1-2-2-1-1-1-2222-2-211-1-111-1-111−2i−2i2i2i1-1iiii−i−i−i−i0000−i3i3i3−i3−333−300000000
χ382222-1-2-2-1-1-1-2222-2-211-1-111-1-111−2i−2i2i2i1-1iiii−i−i−i−i0000i3−i3−i3i33−3−3300000000
χ394444-244-2-2-24-4-44-4-4-2-222-2-2-2-2220000220000000000000000000000000000
χ404444-244-2-2-2-4-44-44-422-2-2-2-222-2-20000220000000000000000000000000000
χ414444-2-4-4-2-2-24-44-4-44-2-2-2-22222220000-220000000000000000000000000000
χ424444-2-4-4-2-2-2-4-4-4444222222-2-2-2-20000-220000000000000000000000000000
χ434-4-4444-4-44-400000000004-400002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ444-4-4444-4-44-400000000004-40000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ454-4-444-44-44-40000000000-4400002-2-22002-22-2-22-2200000000000000000000
χ464-4-444-44-44-40000000000-440000-222-200-22-222-22-200000000000000000000
χ474-4-44-24-42-220000000023−23-220023−232i−2i2i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000
χ484-4-44-24-42-220000000023−23-220023−23−2i2i−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000
χ494-4-44-24-42-2200000000−2323-2200−23232i−2i2i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000
χ504-4-44-24-42-2200000000−2323-2200−2323−2i2i−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000
χ514-4-44-2-442-220000000023−232-200−23232-2-2200−1−31+3−1+31−31+3−1−31−3−1+300000000000000000000
χ524-4-44-2-442-220000000023−232-200−2323-222-2001+3−1−31−3−1+3−1−31+3−1+31−300000000000000000000
χ534-4-44-2-442-2200000000−23232-20023−232-2-2200−1+31−3−1−31+31−3−1+31+3−1−300000000000000000000
χ544-4-44-2-442-2200000000−23232-20023−23-222-2001−3−1+31+3−1−3−1+31−3−1−31+300000000000000000000
χ5588-8-8800-8-8800000000000000000000000000000000000000000000000000
χ5688-8-8-40044-400000000000043−43000000000000000000000000000000000000
χ5788-8-8-40044-4000000000000−4343000000000000000000000000000000000000
χ588-88-88008-8-800000000000000000000000000000000000000000000000000
χ598-88-8-400-444000000−4i34i3000000000000000000000000000000000000000000
χ608-88-8-400-4440000004i3−4i3000000000000000000000000000000000000000000

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