Finite Group Databasebeta

← Group #10698116

Character table — Group #10698116

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order12222222344666244466661212121212124444612121212121212121244881212121224242424444444442488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-2-22222-2-2-22222-2-2-2-2-2-200002-20000000000000000000022-2-200000000
χ10222222222-2-22222-2-2-22222-2-2-2-2-2-200002-200000000000000000000-2-22200000000
χ1122222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1222222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1322222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ1422222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ15222222-2-2222222-22-2-2-2-2222222-2-20000-2-200000000000000000000000000002-200
χ16222222-2-2222222-22-2-2-2-2222222-2-20000-2-20000000000000000000000000000-2200
χ17222222-2-22-2-2222-2-222-2-222-2-2-2-22222-2-2-222222-2-2-2-2000000000000000000000000
χ18222222-2-22-2-2222-2-222-2-222-2-2-2-222-2-222-22-2-2-2-22222000000000000000000000000
χ19222222-2-2-1-2-2-1-1-1-2-22211-1-11111-1-122-2-21-1-1-1-1-111110000−i3i3−i3i3−i3−i3i3i3000000000000
χ20222222-2-2-1-2-2-1-1-1-2-22211-1-11111-1-122-2-21-1-1-1-1-111110000i3−i3i3−i3i3i3−i3−i3000000000000
χ21222222-2-2-1-2-2-1-1-1-2-22211-1-11111-1-1-2-2221-11111-1-1-1-10000−i3i3−i3i3i3i3−i3−i3000000000000
χ22222222-2-2-1-2-2-1-1-1-2-22211-1-11111-1-1-2-2221-11111-1-1-1-10000i3−i3i3−i3−i3−i3i3i3000000000000
χ232222-2-222222222-2-22-222-2-222-2-2-2-20000-22000000002-200-2-2220000000000000000
χ242222-2-222222222-2-22-222-2-222-2-2-2-20000-2200000000-220022-2-20000000000000000
χ252222-2-2222-2-2222-22-2222-2-2-2-222220000-2-200000000000000000000000022-2-20000
χ262222-2-2222-2-2222-22-2222-2-2-2-222220000-2-2000000000000000000000000-2-2220000
χ272222-2-222-122-1-1-1-2-22-2-1-111-1-1111100001-133−3−333−3−32-20011-1-13−33−3000000000000
χ282222-2-222-122-1-1-1-2-22-2-1-111-1-1111100001-133−3−333−3−3-2200-1-111−33−33000000000000
χ292222-2-222-122-1-1-1-2-22-2-1-111-1-1111100001-1−3−333−3−3332-20011-1-1−33−33000000000000
χ302222-2-222-122-1-1-1-2-22-2-1-111-1-1111100001-1−3−333−3−333-2200-1-1113−33−3000000000000
χ312222-2-2-2-22222222-2-22-2-2-2-222-2-22200002-20000000000000000000000000000002-2
χ322222-2-2-2-22222222-2-22-2-2-2-222-2-22200002-2000000000000000000000000000000-22
χ332222-2-2-2-22-2-2222222-2-2-2-2-2-2-222-2-200002200000000002i−2i00002i−2i−2i2i000000000000
χ342222-2-2-2-22-2-2222222-2-2-2-2-2-2-222-2-20000220000000000−2i2i0000−2i2i2i−2i000000000000
χ352222-2-2-2-2-1-2-2-1-1-1222-2111111-1-1110000-1-133−3−3−3−333002i−2ii3−i3−i3i3−iii−i000000000000
χ362222-2-2-2-2-1-2-2-1-1-1222-2111111-1-1110000-1-133−3−3−3−33300−2i2i−i3i3i3−i3i−i−ii000000000000
χ372222-2-2-2-2-1-2-2-1-1-1222-2111111-1-1110000-1-1−3−33333−3−3002i−2i−i3i3i3−i3−iii−i000000000000
χ382222-2-2-2-2-1-2-2-1-1-1222-2111111-1-1110000-1-1−3−33333−3−300−2i2ii3−i3−i3i3i−i−ii000000000000
χ3944444444-2-4-4-2-2-24-4-4-4-2-2-2-22222220000-2200000000000000000000000000000000
χ40444444-4-4-244-2-2-2-44-4-422-2-2-2-2-2-22200002200000000000000000000000000000000
χ414444-4-444-2-4-4-2-2-2-44-44-2-22222-2-2-2-200002200000000000000000000000000000000
χ424444-4-4-4-4-244-2-2-24-4-442222-2-222-2-20000-2200000000000000000000000000000000
χ4344-4-4000044-4-4-44000000004-40000000000000000000000000000002i−2i2i−2i00000000
χ4444-4-4000044-4-4-44000000004-4000000000000000000000000000000−2i2i−2i2i00000000
χ4544-4-400004-44-4-4400000000-440000000000000000000000000000002i−2i−2i2i00000000
χ4644-4-400004-44-4-4400000000-44000000000000000000000000000000−2i2i2i−2i00000000
χ474-44-4004-4400-44-400004-4000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ484-44-4004-4400-44-400004-400000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ494-44-4004-4-2002-220000-22000023−2323−232i−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−ζ11000000000000000000000000
χ504-44-4004-4-2002-220000-22000023−2323−23−2i2i−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+ζ11000000000000000000000000
χ514-44-4004-4-2002-220000-220000−2323−23232i−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−ζ11000000000000000000000000
χ524-44-4004-4-2002-220000-220000−2323−2323−2i2i−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+ζ11000000000000000000000000
χ534-44-400-44400-44-40000-44000000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ544-44-400-44400-44-40000-4400000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ554-44-400-44-2002-2200002-2000023−23−23232i−2i−2i2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ564-44-400-44-2002-2200002-2000023−23−2323−2i2i2i−2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ574-44-400-44-2002-2200002-20000−232323−232i−2i−2i2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ584-44-400-44-2002-2200002-20000−232323−23−2i2i2i−2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ594-4-444-4004004-4-40000004-40000000000000000000000000000000000002i−2i2i−2i0000
χ604-4-444-4004004-4-40000004-4000000000000000000000000000000000000−2i2i−2i2i0000
χ614-4-44-44004004-4-4000000-440000000000000000000000000000000000002i−2i−2i2i0000
χ624-4-44-44004004-4-4000000-44000000000000000000000000000000000000−2i2i2i−2i0000
χ6388-8-80000-48-844-400000000-44000000000000000000000000000000000000000000
χ6488-8-80000-4-8844-4000000004-4000000000000000000000000000000000000000000
χ658-8-888-800-400-444000000-4400000000000000000000000000000000000000000000
χ668-8-88-8800-400-4440000004-400000000000000000000000000000000000000000000

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